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The Shifted Boundary Method (SBM) belongs to the class of unfitted (or immersed, or embedded) finite element methods, and relies on reformulating the original boundary value problem over a surrogate (approximate) computational domain. The surrogate domain is constructed so as to avoid cut cells and the associated problematic implementation and numerical integration issues. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions: hence the name of the method, that shifts the location and values of the boundary conditions. In this article, we extend the SBM to the simulation of incompressible Stokes flow, by appropriately weighting its variational form with the elemental volume fraction of active fluid. This approach allows to drastically reduce spurious pressure oscillations in time, which are produced if the total volume of active fluid were to change abruptly over a time step. The proposed Weighted SBM (W-SBM) exactly preserves states of hydrostatic equilibrium, and induces small mass and momentum conservation errors, which converge as the grid is refined. This is in analogy to cutFEMs and related unfitted approaches, which rely on an affine representation of cut boundaries. We demonstrate the robustness and accuracy of the proposed method with an extensive suite of two-dimensional tests. • The Weighted Shifted Boundary Method (W-SBM) is extended to Stokes flow with moving boundaries. • New no-slip conditions are developed, with optimal accuracy. • Spurious pressure oscillations in time are drastically reduced by volume fraction weighting. • The mass and momentum conservation errors rapidly decay as the mesh are refined. • Extensive numerical testing is performed, including the limit of extremely small time steps. [ABSTRACT FROM AUTHOR]

Immersed boundary methods have seen an enormous increase in popularity over the past two decades, especially for problems involving complex moving/deforming boundaries. In most cases, the boundary conditions on the immersed body are enforced via forcing functions in the momentum equations, which in the case of fractional step methods may be problematic due to: i) creation of slip-errors resulting from the lack of explicitly enforcing boundary conditions on the (pseudo-)pressure on the immersed body; ii) coupling of the solution in the fluid and solid domains via the Poisson equation. Examples of fractional-step formulations that simultaneously enforce velocity and pressure boundary conditions have also been developed, but in most cases the standard Poisson equation is replaced by a more complex system which requires expensive iterative solvers. In this work we propose a new formulation to enforce appropriate boundary conditions on the pseudo-pressure as part of a fractional-step approach. The overall treatment is inspired by the ghost-fluid method typically utilized in two-phase flows. The main advantage of the algorithm is that a standard Poisson equation is solved, with all the modifications needed to enforce the boundary conditions being incorporated within the right-hand side. As a result, fast solvers based on trigonometric transformations can be utilized. We demonstrate the accuracy and robustness of the formulation for a series of problems with increasing complexity. • Most fractional step implementations of IB methods do not explicitly enforce boundary conditions on the pressure. • Lack of enforcement of boundary conditions to the pressure results to slip-errors on the body. • The new formulation we propose utilizes standard pressure solvers based on FFTs. • Results on a series of flows with increasing complexity show a dramatic improvement compared to existing methods. [ABSTRACT FROM AUTHOR]

This paper introduces a new immersed boundary (IB) method for viscous incompressible flow, based on a Fourier spectral method for the fluid solver and on the nonuniform fast Fourier transform (NUFFT) algorithm for coupling the fluid with the immersed boundary. The new Fourier spectral immersed boundary (FSIB) method gives improved boundary resolution in comparison to the standard IB method. The interpolated velocity field, in which the boundary moves, is analytically divergence-free. The FSIB method is gridless and has the meritorious properties of volume conservation, exact translation invariance, conservation of momentum, and conservation of energy. We verify these advantages of the FSIB method numerically both for the Stokes equations and for the Navier-Stokes equations in both two and three space dimensions. The FSIB method converges faster than the IB method. In particular, we observe second-order convergence in various problems for the Navier-Stokes equations in three dimensions. The FSIB method is also computationally efficient with complexity of O (N 3 log ⁡ (N)) per time step for N 3 Fourier modes in three dimensions. • The FSIB method is gridless and has exact translation invariance. • A divergence-free interpolated velocity field that conserves volume. • Equivalent to the use of a new 'sinc' kernel in the framework of IB method. • Improved boundary resolution and faster convergence rate than the IB method. • Conservation of momentum and conservation of energy. [ABSTRACT FROM AUTHOR]

In this paper we propose an improved three-dimensional immersed boundary method coupled with a finite-difference code to simulate self-propelled phoretic particles in viscous incompressible flows. We focus on the phenomenon of diffusiophoresis which, using the driving of a concentration gradient, can generate a slip velocity on a surface. In such a system, both the Dirichlet and Neumann boundary conditions are involved. In order to enforce the boundary conditions, we propose two improvements to the basic direct-forcing immersed boundary method. The main idea is that the immersed boundary terms are corrected by adding the force of the previous time step, in contrast to the traditional method which relies only on the instantaneous forces in each time step. For the Neumann boundary condition, we add two auxiliary layers inside the body to precisely implement the desired concentration gradient. To verify the accuracy of the improved method, we present problems of different complexity: The first is the pure diffusion around a sphere with Dirichlet and Neumann boundary conditions. Then we show the flow past a fixed sphere. In addition, the motion of a self-propelled Janus particle in the bulk and the spontaneously symmetry breaking of an isotropic phoretic particle are reported. The results are in very good agreements with the data that are reported in previously published literature. • We correct immersed boundary terms through the addition of forces from previous time steps. • The approach departs from traditional methods that rely solely on instantaneous forces, enhancing simulation accuracy. • The study presents a range of validations, from pure diffusion around a sphere to flow past a fixed sphere. • The motion of self-propelled Janus particles and the symmetry breaking of isotropic phoretic particles are explored. • Phoretic particle is a new field that immersed boundary method can be applied to. [ABSTRACT FROM AUTHOR]

This study focuses on obtaining reliable hydrodynamic stresses on the surface of rigid bodies in the simulation of fluid-solid interactions using the diffuse-interface immersed boundary method (IBM). In order to obtain the pressure and velocity gradient information on the immersed boundary, we employ a model to reconstruct the near-boundary fluid flow along the surface normal direction. Different from most existing flow reconstruction models in diffuse-interface IBMs based on the boundary layer approximation, we propose a new reconstruction model relying only on the non-slip velocity and local flow information. With this improvement, the present reconstruction model is theoretically applicable to fluid flows with intermediate Reynolds numbers (with the existence of a laminar boundary layer) and low Reynolds numbers (in the absence of a boundary layer). To examine the validity of the present reconstruction model, we conduct a series of simulations, including the uniform flow past a fixed body and the settling of a rigid body in a quiescent fluid. It is demonstrated that the present reconstruction model has a better performance than existing models in predicting hydrodynamic stresses on the immersed boundary within a wide range of Reynolds numbers from O (1) to O (100). The capability and robustness of the proposed model demonstrate its potential to address fluid-solid interaction problems with a-priori unknown or time-varying Reynolds numbers, such as fully resolved simulations of particle laden flows. [ABSTRACT FROM AUTHOR]

The Immersed Boundary (IB) method of Peskin (1977) [1] is useful for problems that involve fluid-structure interactions or complex geometries. By making use of a regular Cartesian grid that is independent of the geometry, the IB framework yields a robust numerical scheme that can efficiently handle immersed deformable structures. Additionally, the IB method has been adapted to problems with prescribed motion and other PDEs with given boundary data. IB methods for these problems traditionally involve penalty forces which only approximately satisfy boundary conditions, or they are formulated as constraint problems. In the latter approach, one must find the unknown forces by solving an equation that corresponds to a poorly conditioned first-kind integral equation. This operation can therefore require a large number of iterations of a Krylov method, and since a time-dependent problem requires this solve at each step in time, this method can be prohibitively inefficient without preconditioning. This work introduces a new, well-conditioned IB formulation for boundary value problems, called the Immersed Boundary Double Layer (IBDL) method. In order to lay the groundwork for similar formulations of Stokes and Navier-Stokes equations, this paper focuses on the Poisson and Helmholtz equations to introduce the methodology and to demonstrate its efficiency over the original constraint method. In this double layer formulation, the equation for the unknown boundary distribution corresponds to a well-conditioned second-kind integral equation that can be solved efficiently with a small number of iterations of a Krylov method without preconditioning. Furthermore, the iteration count is independent of both the mesh size and spacing of the immersed boundary points. The method converges away from the boundary, and when combined with a local interpolation, it converges in the entire PDE domain. Additionally, while the original constraint method applies only to Dirichlet problems, the IBDL formulation can also be used for Neumann boundary conditions. • Reformulated Immersed Boundary method for double layer integral equations. • Efficient IB constraint method for PDEs with prescribed boundary values. • Well-conditioned IB method resulting from second-kind integral equation formulation. • IB method for Neumann boundary conditions. [ABSTRACT FROM AUTHOR]

We present and analyze a series of benchmark tests regarding the application of the immersed boundary (IB) method to viscoelastic flows through and around non-trivial, stationary geometries. The IB method is widely used to simulate biological fluid dynamics and other modeling scenarios in which a structure is immersed in a fluid. Although the IB method has been most commonly used to model systems involving viscous incompressible fluids, it also can be applied to visoelastic fluids and has enabled the study of a wide variety of dynamical problems including the settling of vesicles and the swimming of elastic filaments in fluids modeled by the Oldroyd-B constitutive equation. In the viscoelastic context, however, relatively little work has explored the accuracy or convergence properties of this numerical scheme. Herein, we present benchmarking results for an IB solver applied to viscoelastic flows in and around non-trivial geometries using either the idealized Oldroyd-B constitutive model or the more physically realistic, polymer-entanglement-based Rolie-Poly constitutive equations. We use two-dimensional numerical test cases along with results from rheology experiments to benchmark the IB method and compare it to more complex finite element and finite volume viscoelastic flow solvers. Additionally, we analyze different choices of regularized delta function and relative Lagrangian grid spacings which allow us to identify and recommend the key choices of these numerical parameters depending on the present flow regime. • The Immersed Boundary method is applied to viscoelastic flows around non-trivial, stationary geometries. • Computational results are compared to previous numerical benchmarks and macrorheology experiments. • Choices of relative Lagrangian grid spacings and delta functions are analyzed, with recommendations for current flow regimes. [ABSTRACT FROM AUTHOR]

• Dynamics of soft robotic fish driven by dielectric elastomer actuators is studied. • A large-deformation fluid–structure interaction model for analyzing the fish body is presented. • The effects of key parameters on the hydrodynamic propulsion performance of the bionic robotic fish are presented and discussed. Dielectric elastomer (DE) is an intelligent and pliable material that exhibits significant deformation when subjected to an electric field. It possesses attributes such as remarkable strain, exceptional energy density, rapid responsiveness, and minimal weight, making it uniquely advantageous in the propulsion of bionic fish. Due to the nonlinearity and large deformation characteristics of DEs, it is challenging to accurately describe their complex deformations. The absolute nodal coordinate formulation (ANCF) possesses notable advantages in precisely depicting phenomena entailing substantial deformation and displacement. This paper focuses on the study of a bionic robotic fish driven by dielectric elastomer actuators (DEAs) based on body/caudal fin (BCF) propulsion, wherein the fish body is delineated as a laminated beam structure. By combining the ANCF higher-order beam element with the DE constitutive model and the neo-Hookean hyperelastic constitutive model, the dynamic equations of the laminated beam are derived. The interaction between the bionic fish and the fluid is effectively handled through the implementation of the immersed boundary - lattice Boltzmann method (IB-LBM), and by combining ANCF with IB-LBM, the dynamic responses of the fish under voltage excitation and fluid resistance are simulated and analyzed. This study would contribute to the exploration of the intricate mechanism behind the substantial amplitude motion of bionic robotic fish driven by DEAs, yielding valuable insights for further research endeavors. [ABSTRACT FROM AUTHOR]

[Display omitted] Aggregate structure is conditioned by a balance of cohesive forces between primary particles and hydrodynamic forces induced by the surrounding flow. Numerical simulations for different ratios between radial and tangential components of cohesive forces to hydrodynamic forces should highlight the role of the each force in aggregate restructuring under shear flow. Aggregates sharing similar morphological characteristics were algorithmically created. The forces between primary particles were accounted for using models taken from the literature. Aggregates with different cohesive forces were then submitted to shear by imposing a shear stress in the liquid phase. Hydrodynamic forces were calculated following two approaches: first, with a free draining approximation to extract general trends, then with immersed boundaries in a lattice Boltzmann flow solver to fully resolve the flow and particle dynamics. Aggregate structural changes were tracked over time and their stable final size, or eventual breakage, was recorded. Their final structure was found to depend little on normal cohesive forces but is strongly impacted by tangential forces. Normal forces, however, strongly affect breakage probability. Furthermore, resistance to deformation at the aggregate scale induces a flow disturbance that reduces drag forces compared to the free-draining approximation, significantly impacting aggregate restructuring. [ABSTRACT FROM AUTHOR]

The projection immersed boundary method calculates boundary forces (i.e., surface stresses) from velocity constraints without introducing additional timestep restrictions. However, the projection method generally fails to produce boundary forces that converge to the actual physical surface stresses when the grid is refined. In most cases, the boundary forces show spurious oscillation. This spurious oscillation is particularly violent when the Lagrangian-to-Eulerian grid spacing ratio is small. As a result, the traditional projection method may encounter problems in fluid-structural interaction (FSI) simulations where accurate boundary forces are needed. To address these challenges, we propose a regularized projection method using (generalized) Tikhonov regularization techniques. The regularized projection method yields smoother boundary force solutions that closely approximate the actual boundary force distributions for a wider range of Lagrangian-to-Eulerian grid spacing ratios. The boundary force shows first order convergence with properly chosen parameters. We demonstrate the effectiveness and accuracy of our approach through various test cases. • Proposed a Tikhonov regularized projection immersed boundary method. • Accurately computed body forces, eliminating spurious oscillations. • Demonstrated convergence of body forces with test problems. • Validated applicability to FSI problems with Turek-Hron problems. [ABSTRACT FROM AUTHOR]

The pathogenesis and progression of calcific aortic stenosis pose a significant challenge in medical science due to the intricate nature of blood fluid dynamics. To better understand this crucial phenomenon, this study investigates the physiological behaviors of aortic valves with varying degrees of lesions and ambient flow conditions using an in-house CFD solver, CgLES-Y code. The code is validated by simulating two-dimensional valve opening and closure, followed by the extension to three-dimensional symmetrically simplified valve dynamics. The simulation results exhibit great agreement with other numerical, experimental and clinical data. Patient-specific models of the aortic root and inner valve geometries are developed based on CT images. Analysis of fluid dynamics traits, configuration properties and leaflet stress is performed for both normal and calcified aortic valves during the systolic and diastolic periods. The study further examines the impact of calcium deposition on abnormal flow fields and leaflet motion, which indicates that calcium deposition increases the tensional burden on healthy leaflets, therefore, the microcosmic increase in valve modulus leads to global damage extending from the root to the tip, whereas macroscopic calcification primarily induces damage in the vicinity of the calcium compound. Additionally, the generation of additional vortices on the valve surface and sinus lumen heightens the likelihood of calcium accumulation. [ABSTRACT FROM AUTHOR]

The fluid–structure–acoustics interaction of flexible flapping wings is numerically studied by using an immersed boundary method at a Mach number of 0.1. In this study, a wing flapping in a uniform flow with prescribed leading edge motion is considered. Apart from rigid wings, flexible wings of various bending rigidities and mass ratios are also examined. By using a direct numerical simulation technique, the sound generation mechanism is identified. The numerical results show that the wing with combined translational and rotational motion generates smaller sounds than the translating wing, and larger rotational angles transform the dipole sound to a monopole one. Similar sound fields are observed among all these wings, except that the direction of the sound shifts to the downstream for large flexible wings. Frequency analysis shows that the sound is dominated by the flapping frequency and two times of the flapping frequency in the vertical and horizontal directions, respectively. The results also show that the thrust increases first then decreases with bending rigidity for all three mass ratios considered, and the lighter wing suffers more decrease. However, the fluctuating pressure for the three mass ratios varies significantly. Specifically, it increases significantly with the decreasing bending rigidity when the structural inertia is dominating at m ∗ = 5. 0 ; but it experiences a reduction contrarily when the aerodynamics becomes dominant at m ∗ = 0. 5 ; for the medium mass ratio at m ∗ = 1. 0 , no significant effects are observed. The comparisons indicate that the flexible wing with a lower mass ratio (e.g. m ∗ = 0. 5) and a medium flexibility (e.g. ω ∗ = 0. 3) achieves lower sound generation without significant thrust decrease. In addition, the sound on the windward side is pronounced significantly when the wing is flapping with a stroke plane angle less than 9 0 o . The present results can expand the currently limited database of fluid–structure–acoustics interaction, and also provide an insight for the optimization of flight vehicle using flapping wing. [ABSTRACT FROM AUTHOR]

A sharp immersed boundary computational aeroacoustic simulation approach for open-rotor direct noise predictions is presented. A specific feature of the finite-difference based immersed boundary method is that the stencil coefficients in the vicinity of the immersed boundary are determined in such a way that the stability of the numerical scheme is improved. The characteristics of this immersed boundary method are discussed for acoustic scattering and the treatment of moving boundaries, such as accounting for freshly cleared and dead cells, efficient geometry queries and efficient computation of irregular boundary stencils and point clouds in the vicinity of the immersed boundary. It is shown that the numerical error when considering moving boundary problems consistently scales with the order of accuracy of the boundary discretization. Finally, the method is applied to simulate the flow around a contra-rotating open rotor at take-off and cruise conditions where experimental data is available for comparison. Excellent agreement for the noise predictions of the contra-rotating open rotor system are obtained between the numerical simulations and the experimental noise measurement. • Sharp IBM for moving boundary problems utilizing optimized irregular finite difference boundary operators. • Detailing methodologies used to efficiently simulate large-scale moving boundary problems. • Numerical error analysis for moving boundary problem with an immersed boundary method for solving the compressible Navier-Stokes equations. • One of a kind open-rotor noise simulation employing sharp IBM and detailed comparison to experimental data. [ABSTRACT FROM AUTHOR]

Abstract In the frameworks of immersed boundary method (IBM) and finite volume method (FVM), an implicit heat flux correction-based IB-FVM is proposed for thermal flows with Neumann boundary conditions. With the use of a fractional-step technique, the preconditioned Navier–Stokes (N–S) equations are solved by the FVM to obtain the intermediate solution in the prediction step and the heat flux is corrected by enforcing the Neumann condition in the correction step. Different from existing IBMs, the cell face centers are defined as the Eulerian points due to the heat flux computation at each face in the FVM. The Neumann condition is implemented in such a way that the interpolated temperature gradient is equal to the specified boundary value at the same point when the corrected gradient field is interpolated from the face centers to the Lagrangian points. To achieve an implicit algorithm, the temperature derivative corrections at the Lagrangian points are set as unknowns and a system of algebraic equations is established by constructing hybrid thin-plate splines (TPS) interpolation/delta function distribution. In the derivative interpolation process, the much more accurate TPS is introduced because the use of cosine delta function yields a less accurate solution. After the distribution process, the heat flux correction of a fluid cell is evaluated by using the solved temperature derivative corrections at the face centers, but that of a solid cell is calculated by using their additive inverses to supplement the same amount of heat flux into the solid domain as that flowing into the fluid domain across the boundary. Finally, the heat flux of a cell is corrected by adding the correction to the intermediate value and the corrected heat flux is utilized to solve the N–S equations in the prediction step. As compared with the available implicit IBMs for Neumann conditions, the present method avoids the introduction of auxiliary layers of Lagrangian points as well as the approximate conversion from the Neumann to Dirichlet condition and thus is suitable for an arbitrary geometry. The proposed method is verified by simulating several benchmark thermal flows with Neumann conditions, the natural convection in an annulus and the steady or unsteady forced convection over a stationary or oscillating cylinder. All the computed results agree well with the literature data. Highlights • An implicit heat flux correction-based IB-FVM is proposed using TPS interpolation/delta function distribution. • Different from conventional IBM, the cell face centers are defined as the Eulerian points. • The heat flux of a solid cell is corrected using the additive inverses of the temperature derivative corrections. [ABSTRACT FROM AUTHOR]

Abstract In this Short Note, a graph-partitioning framework for a sharp-interface immersed boundary method is proposed so as to increase its computational efficiency for simulating internal flows on large-scale parallel computers. Immersed boundary methods are generally inefficient for internal flows with complex geometries due to the larger proportion of grid points that fall outside the fluid domain for such configurations. The graph-partitioning framework proposed here enables the solver to effectively ignore these points and focus the computation on the active points inside the fluid domain. A novel coarsening-partitioning process is proposed to ensure that sufficient overlapping layers are available at the sub-domain interfaces to accommodate computational stencils associated with the discretization as well as the sharp-interface boundary conditions. The benchmark test shows that the adoption of the graph topology reduces the computational cost (wall-time and memory cost) substantially. Moreover, the computational cost is shown to only scale with the number of computationally active grid points. The capability of the graph-partitioned solver is further demonstrated by simulating the flow inside an arterial network, a configuration which would otherwise be out of reach for most immersed boundary methods. Highlights • A graph-based parallel framework is developed for immersed boundary methods. • It enables efficient solution of internal flows in the cardiovascular system. • Benchmark tests show significant performance improvement. [ABSTRACT FROM AUTHOR]

The flow-induced deformation of a viscoelastic thin plate attached to the lee side of a circular cylinder subjected to laminar flow is numerically investigated. An in-house fluid–structure interaction solver couples the sharp-interface immersed boundary method for fluid dynamics with a finite-element method for structural dynamics. Extending published results on elastic materials, the Standard Linear Solid (SLS) model is used to represent viscoelasticity of the plate, governed by the following two parameters: (a) the ratio of the non-equilibrium to equilibrium Young's modulus (R) , and (b) the ratio of dimensionless material damping to the dimensionless non-equilibrium Young's modulus (τ). The focus of the present study is to examine the dynamic response of the viscoelastic plate at Reynolds number of R e = 100. The amplitude and the time to achieve a dynamic steady state of a plate with 0. 1 < R < 5 and 0. 1 < τ < 10 have been investigated. The plate attains a self-sustained time-periodic oscillation with a plateau amplitude for the range of R = [0.1–5] for all values of τ. The dimensionless tip displacement amplitude (A Y , t i p) is found to be a non-monotonic function of τ. When the forcing frequency (vortex shedding frequency) is lesser (greater) than the natural frequency (considering the equilibrium Young modulus) of the plate, A Y , t i p decreases (increases) asymptotically. The theoretical analysis of a simple spring–mass–dashpot model of SLS is undertaken to understand the effect of sinusoidal forcing on the plate dynamics. Analytical predictions show general agreement with the non-monotonic behaviour of the numerically computed A Y , t i p. The results suggest that careful tuning of the damping may be effectively employed to enhance power output for energy extraction applications or to suppress flow-induced vibration when it is detrimental to the structure. [ABSTRACT FROM AUTHOR]

Highlights • A model that accurately reconstructs the forces on an immersed body is proposed. • It is based on the boundary layer (BL) equations and accounts the effects of surface curvature. • The model requires numerical resolution that places 1 to 2 points in the boundary layer around the particle. • It is applicable to simulations of turbulence interacting with particles of arbitrary shape. • Several 2D and 3D benchmark flows are in excellent agreement with reference data. Abstract In this work we propose a hydrodynamic stress model that accurately reconstructs the forces on an immersed body, with application to the simulation of turbulence interacting with finite-size particles of arbitrary shape. The proposed model is local and is based on the boundary layer approximation, where the effects of surface curvature on the pressure variation are accounted for. Numerical experiments show that the model requires about one or two grid points within the boundary layer to accurately reconstruct the hydrodynamic force distribution. This reduces significantly the cost of resolving the flow field around the particles. The accuracy of the proposed model is evaluated in a variety of flows with increasing complexity. In particular, results for the flows over stationary and oscillating circular cylinders, free falling cylinders and spheres, and the interaction of turbulence with spheres and ellipsoids will be presented. [ABSTRACT FROM AUTHOR]

Abstract This paper presents an immersed boundary method (IBM) to model the behaviour of solid–fluid interfaces in incompressible flows on non-conforming, unstructured meshes. Based on a smooth-interface direct forcing formulation, the proposed forcing method directly and implicitly uses the discretised momentum equations to evaluate the source terms required to enforce a no-slip condition on the boundary. The IBM is derived for a finite-volume framework with an implicit pressure-velocity coupling and a colocated variable arrangement, to enable application in complex domains. The novel framework is applied to flows with stationary and moving IBs on both Cartesian and tetrahedral meshes, and the results are compared to and validated with findings reported in the literature. The results demonstrate that the proposed formulation results in an accurate enforcement of the no-slip condition on the IB at every time-step, even for flows with strong transient behaviour and high velocity and pressure gradients. The results are similar to or better than those obtained with other methods that can only be applied on Cartesian meshes. The current method is shown to accurately preserve local continuity in the vicinity of the IB, ensuring local and global mass conservation in addition to satisfying the local no-slip condition. Moreover, the proposed forcing framework shows good results for unstructured meshes, with a similar accuracy as obtained on Cartesian meshes. Highlights • Development of Immersed Boundary Method for unstructured meshes with a co- located variable arrangement. • Derivation using the analytical form of the discretised momentum equations. • Suitable for fully-coupled pressure-velocity solver framework. • Consistent treatment of spreading and interpolation, leading to the exact enforcement of the no-slip condition. • Comprehensive analysis, comparison, and validation using representative test cases. [ABSTRACT FROM AUTHOR]

Highlights • To our knowledge, this is the first numerical work for the investigations of Newtonian vesicle dynamics in Oldroyd-B fluid. • The inclination angle and tank-treading frequency of the N/O fluid case are comparably smaller than the ones in N/N fluid. • In matched viscosity N/O fluid, the vesicle inclination angle in TT regime decreases with increasing Weissenberg number. • In unmatched viscosity N/O fluid, most surprisingly, the negative inclination angle is found in TT regime. • The inertia enables the vesicle to undergo TT-TB-TT transition as the Reynolds number increases. Abstract In this paper, a two-dimensional immersed boundary method is developed to simulate the dynamics of Newtonian vesicle in viscoelastic Oldroyd-B fluid under shear flow. The viscoelasticity effect of extra stress is well incorporated into the immersed boundary formulation using the indicator function. Our numerical methodology is first validated in comparison with theoretical results in purely Newtonian fluid, and then a series of numerical experiments is conducted to study the effects of different dimensionless parameters on the vesicle motions. Although the tank-treading (TT) motion of Newtonian vesicle in Oldroyd-B fluid under shear flow can be observed just like in Newtonian fluid, it is surprising to find that the stationary inclination angle can be negative without the transition to tumbling (TB) motion. Moreover, the inertia effect plays a significant role that is able to turn the vesicle back to positive inclination angle through TT-TB-TT transition as the Reynolds number increases. To the best of our knowledge, this is the first numerical work for the detailed investigations of Newtonian vesicle dynamics suspended in viscoelastic Oldroyd-B fluid. We believe that our numerical results can be used to motivate further studies in theory and experiments for such coupling vesicle problems. [ABSTRACT FROM AUTHOR]

Abstract The direct-forcing immersed boundary is widely adopted to study particle-laden flows. The effective hydrodynamic diameter of the particle is much or less overestimated by the original immersed boundary method, depending on the particle Reynolds number and grid resolution. In this paper, we propose an improved method to dynamically correct the effective hydrodynamic diameter by retracting inward the Lagrangian points to varying distances. The retraction distance is determined by querying a function fitted in this paper. The improved method is tested and validated by several cases, including falling of a spherical particle under gravity, the uniform flow past two stationary particles and the drafting-kissing-tumbling phenomenon of two settling particles. It turns out the improved method not only provides better results for the drag force but also predicts the flow field more accurately. What's more, due to the insensitivity to grid resolution, the improved method is suitable for simulating large-scale fluid–particle systems such as fluidized bed, which are computationally expensive. Highlights • Optimal retraction distance of Lagrangian points is proposed for direct-forcing immersed boundary method. • The effective hydrodynamic diameter is dynamically corrected. • Higher accuracy is achieved for both drag force and flow field. • The improved method is less sensitive to gird resolution. [ABSTRACT FROM AUTHOR]

Abstract The numerical simulation of two-fluid flows with sharp interfaces is a challenging field, not only because of their complicated physical mechanisms, but also because of increased computational cost. An efficient and robust numerical formulation for incompressible two-fluid flows is proposed. Its novelty is the consistent coupling of Fast Direct Solvers (FDS) with the Immersed Boundary (IB) method to represent solid boundaries. Such a coupling offers several advantages. First, it extends the range of applicability of the IB method. Second, it allows the simulation of practical problems in geometrically complicated domains at a significantly reduced cost. Third, it can shed light on regions of the parametric space which are considered out of reach, or even impossible today. Instead of using a conventional variable coefficient pressure Poisson equation, a pressure-correction scheme is suggested for the solution of a constant coefficient Poisson equation for the pressure difference, extending the novel work of Dodd and Ferrante [8]. The conservative Level-set (LS) method is used to track the interface between the two fluids. Appropriate schemes, based on the local directional Ghost Cell Approach (GCA) are proposed, in order to satisfy the boundary conditions (BCs) of the pressure and the LS function around the IB. The accuracy, robustness, and performance of the proposed method is demonstrated by several validations against conventional approaches and experiments. The results verify that the pressure BCs are properly recovered along the IB solid interface, while a non-smooth pressure field is also allowed across the solid obstacle. The accuracy of the method was found to be 2nd-order, both in time and space. The performance of the proposed method is compared against the conventional approach using a multigrid iterative solver. The impact of the time-step on the accuracy of the constant coefficient approach is examined. Results show that the final speed-up strongly depends on the specific physical and numerical parameters such as the density ratio or the Reynolds number. It is demonstrated that for the range of parameters examined, speed-up factors of 100–10 can be achieved for density ratios of 10–1000 respectively. Highlights • Coupling the Immersed Boundary method with Fast Direct Solvers for incompressible two-fluid flows. • Proposing a two-fluid pressure-correction scheme for a constant coefficient Poisson equation. • Validated for low and high density/viscosity ratios. • Same accuracy with variable coefficient Poisson at reduced computational cost. • Achieving speed-up factors of 10–100 for density ratios of 1000–10. [ABSTRACT FROM AUTHOR]

Abstract We present a dimensionally split method for computing solutions to the compressible Navier–Stokes equations on Cartesian cut cell meshes. The method is globally second order accurate in the L 1 norm, fully conservative, and allows the use of time steps determined by the regular grid spacing. We provide a description of the three-dimensional implementation of the method and evaluate its numerical performance by computing solutions to a number of test problems ranging from the nearly incompressible to the highly compressible flow regimes. All the computed results show good agreement with reference results from theory, experiment and previous numerical studies. To the best of our knowledge, this is the first presentation of a dimensionally split cut cell method for the compressible Navier–Stokes equations in the literature. Highlights • A Cartesian cut cell method is presented for the compressible Navier–Stokes equations. • The method is dimensionally split and simple to implement. • The scheme is fully conservative and globally second order accurate in the L 1 norm. • Numerical results are presented for a wide range of multi-dimensional test problems. [ABSTRACT FROM AUTHOR]

Abstract A discrete unified gas kinetic scheme (DUGKS) coupled with the immersed boundary (IB) method is developed to perform interface-resolved simulation of particle-laden flows. The present method (IB-DUGKS) preserves the respective advantages of the IB and DUGKS, i.e., the flexibility and efficiency for treating complex flows, and the robustness and low numerical-dissipation. In IB-DUGKS, the IB method is used to treat the fluid–solid interfaces and the DUGKS is applied to simulate the fluid flow, making use of the Lagrangian and Eulerian meshes, respectively. Those two meshes are fully independent, which contributes to the avoidance of grid regeneration when a solid particle moves. Specifically, in the present implementation of IB-DUGKS, the no-slip boundary condition at the particle surface is accurately enforced by introducing an efficient iterative forcing algorithm, and the IB force induced by the particle boundary is conveniently incorporated into the DUGKS with the Strang–Splitting scheme. The accuracy of the IB-DUGKS is first verified in the flows past a stationary cylinder and an oscillating cylinder in a quiescent fluid. After that, several well-established two- and three-dimensional particulate flow problems are simulated, including the sedimentation of a particle and the DKT dynamics of two particles in a channel, and a group of particles settling in an enclosure. In all test cases, the results are in good agreement with the data available in the literature, demonstrating that the proposed IB-DUGKS is a promising tool for simulating particulate flows. Highlights • IBM is successfully combined with DUGKS and the IB-DUGKS is proposed. • Force term is conveniently absorbed into DUGKS with Strang–Splitting scheme. • Application range of DUGKS is extended to moving boundary problems. • Three dimensional particle suspension flows are implemented. • Versatility and efficiency of IB-DUGKS is demonstrated in the simulations. [ABSTRACT FROM AUTHOR]

Abstract In this paper we propose and test the validity of simple and easy-to-implement algorithms within the immersed boundary framework geared towards large scale simulations involving thousands of deformable bodies in highly turbulent flows. First, we introduce a fast moving least squares (fast-MLS) approximation technique with which we speed up the process of building transfer functions during the simulations which leads to considerable reductions in computational time. We compare the accuracy of the fast-MLS against the exact moving least squares (MLS) for the standard problem of uniform flow over a sphere. In order to overcome the restrictions set by the resolution coupling of the Lagrangian and Eulerian meshes in this particular immersed boundary method, we present an adaptive Lagrangian mesh refinement procedure that is capable of drastically reducing the number of required nodes of the basic Lagrangian mesh when the immersed boundaries can move and deform. Finally, a coarse-grained collision detection algorithm is presented which can detect collision events between several Lagrangian markers residing on separate complex geometries with minimal computational overhead. Highlights • Fast algorithms within the immersed boundary method for multiphase flows. • Fast moving least squares approximation to reduce computational cost. • Adaptive Lagrangian mesh refinement. • Coarse-grained collision detection algorithm. [ABSTRACT FROM AUTHOR]

Abstract A novel computational framework which combines the lattice Boltzmann method (LBM) and an improved immersed boundary method (IBM) based on a dynamic geometry-adaptive Cartesian grid system is introduced for the fluid–structure interaction (FSI) problems at moderate and high Reynolds numbers. In this framework, the fluid dynamics is obtained by solving the discrete lattice Boltzmann equation. The boundary conditions at the fluid–structure interfaces are handled by an improved IBM based on a feedback scheme, which drives the predicted flow velocity (calculated after the LBM stream process without the IBM body force) near the immersed boundaries to match the solid velocity. In the present IBM, the feedback coefficient is mathematically derived and explicitly approximated. The Lagrangian force density is divided into two parts: one is the traction caused by the predicted flow velocity, and the other is caused by the acceleration of the immersed boundary. Such treatment significantly enhances the numerical stability for modelling FSI problems involving small structure-to-fluid mass ratios. A novel dynamic geometry-adaptive refinement is applied to provide fine resolution around the immersed geometries and coarse resolution in the far field. The overlapping grids between two adjacent refinements consist of two layers. In order to enhance the numerical stability, two-layer "ghost nodes" are generated within the immersed body domain which is a non-fluid area. The movement of fluid–structure interfaces only causes adding or removing grids at the boundaries of refinements and consequently a high mesh-update efficiency is guaranteed. Finally, large eddy simulation models are incorporated into the framework to model turbulent flows at relatively high Reynolds numbers. Several validation cases, including an impulsively started flow over a vertical plate, flow over stationary and oscillating cylinders, flow over flapping foils, flexible filaments in a uniform flow, turbulent flow over a wavy boundary, flow over a stationary sphere and a dragonfly in hovering flight, are conducted to verify the accuracy and fidelity of the present solver over a range of Reynolds numbers. Highlights • An adaptive IB–LBM–LES method is developed. • The IBM feedback coefficient is derived and approximated. • The Lagrangian force is divided into predicted flow and IB acceleration tractions. • The method can perform weakly coupled FSI simulations for small mass ratios. • Several validation cases are conducted. [ABSTRACT FROM AUTHOR]

Abstract Immersed boundary (IB) methods deal with incompressible visco-elastic solids interacting with incompressible viscous fluids. A long-standing issue of IB methods is the challenge of accurately imposing the incompressibility constraint at the discrete level. We present the divergence-conforming immersed boundary (DCIB) method to tackle this issue. The DCIB method leads to completely negligible incompressibility errors at the Eulerian level and various orders of magnitude of increased accuracy at the Lagrangian level compared to other IB methods. Furthermore, second-order convergence of the incompressibility error at the Lagrangian level is obtained as the discretization is refined. In the DCIB method, the Eulerian velocity–pressure pair is discretized using divergence-conforming B-splines, leading to inf–sup stable and pointwise divergence-free Eulerian solutions. The Lagrangian displacement is discretized using non-uniform rational B-splines, which enables to robustly handle large mesh distortions. The data transfer needed between the Eulerian and Lagrangian descriptions is performed at the quadrature level using the same spline basis functions that define the computational meshes. This conduces to a fully variational formulation, sharp treatment of the fluid–solid interface, and a 0.5 increase in the convergence rate of the Eulerian velocity and the Lagrangian displacement measured in L 2 norm in comparison with using discretized Dirac delta functions for the data transfer. By combining the generalized- α method and a block-iterative solution strategy, the DCIB method results in a fully-implicit discretization, which enables to take larger time steps. Various two- and three-dimensional problems are solved to show all the aforementioned properties of the DCIB method along with mesh-independence studies, verification of the numerical method by comparison with the literature, and measurement of convergence rates. Highlights • We present the divergence-conforming immersed boundary (DCIB) method. • The DCIB method leads to negligible incompressibility errors at the Eulerian level. • The spurious volume change is orders of magnitude smaller than in other IB methods. • The energy conservation is compared with other immersed FSI methods. • The convergence rates of the DCIB method are computed. [ABSTRACT FROM AUTHOR]

Abstract A consistent and conservative immersed boundary method has been developed to accurately and efficiently solve two topics: magnetohydrodynamics flows with a complex boundary and moving boundary problems. Based on a least square interpolation reconstruction method, a unified form of boundary condition is described to handle a single domain situation while a mixed boundary condition is used for coupled conditions of multi-domain. In order to achieve the consistency with a desired wall boundary condition, a so-called approximation-correction procedure is done, and an imposing Neumann boundary condition is discussed with two kinds of different schemes. Besides, a consistent and conservative scheme is implemented to satisfy both the charge and mass conservation laws on cells around the immersed surface. Then, a conservative interpolation is reconstructed for velocity in moving boundary problems. At last, the applied numerical method is validated by stationary and moving boundary cases and an excellent agreement is obtained with good accuracy, efficiency and conservation. Especially, the consistent and conservative immersed boundary method can obtain almost the same accurate results as those from the cut cell technique (Seo and Mittal, 2011) [14] for a moving boundary problem by reducing the spurious pressure. Highlights • A consistent and conservative immersed boundary method has been developed to accurately and efficiently solve two topics of magnetohydrodynamics flows with a complex boundary and moving boundary problems. • A consistent and conservative scheme is implemented to satisfy both the charge and mass conservation laws on cells around the immersed surface, and a conservative interpolation is reconstructed for velocity in moving boundary problems. • The applied numerical method is validated by stationary and moving boundary cases with good accuracy, efficiency and conservation. Especially, the consistent and conservative immersed boundary method can obtain almost the same accurate results as those from the cut cell technique (J.H. Seo, R. Mittal, J. Comp. Phys. 230 (2011) 7347–7363) for a moving boundary problem by reducing the spurious pressure. [ABSTRACT FROM AUTHOR]

Abstract The passive response of a semi-free flexible filament in the wake of a flapping foil is studied numerically Three distinct flapping states are observed for the filament in different vortex streets: flapping between Kármán vortices, flapping outside reversed Kármán vortices and static in compact Kármán vortices. Both the vertical dipole-induced velocity and the transport speed of the vortices determine the filament's flapping motion. A significant drag reduction is obtained for the filament when flapping outside reversed Kármán vortices compared to flapping between vortices. The pitching foil has decreased drag when the downstream filament is static. These passive flapping motions of the filament in different wakes may be beneficial for achieving a better understanding of fish swimming mechanics and behaviors in schools. Graphical abstract Highlights • Three flapping states are observed for the filament in different vortex streets. • The filament flaps between the vortices in the von-Kármán vortex streets. • The filament flaps outside the vortices in the reversed von-Kármán vortex streets. • The filament is static in the compact Kármán vortices. • Vertical dipole-induced velocity and vortex transportation speed affect the states. [ABSTRACT FROM AUTHOR]

Abstract The force components on two circular cylinders in tandem, side-by-side and staggered arrangements and in a uniform incoming flow are investigated systematically with Reynolds number being taken R e = 200. The numerical simulations are undertaken using the lattice Boltzmann method and the boundary condition is imposed though the immersed boundary method. At an intermediate centre-to-centre spacing which is based on the ratio of distance between cylinder centres and the cylinder diameter, the fluid force is periodic and dominated virtually by a single frequency component in the tandem arrangement and is random with a continuous frequency spectrum in the side-by-side arrangement. Here random means that the components of the force are not in the form of discrete frequencies, but are in the form of continuous spectrum. Detailed analysis has been undertaken to show this evolution process with the alignment angle α , which is defined as the angle between the incoming flow direction and the line linking two cylinders. As α increases, the frequency component of the force on each individual cylinder changes from a single value to multiple ones, then to a large number of discrete ones and eventually to a broadband continuous spectrum. The results have important implications to vortex induced vibration and fatigue analysis of the cylinder, which has important applications, such as risers in offshore engineering. Highlights • The present work considers two circular cylinders in various arrangements and in a uniform incoming flow. • Although there is a large amount of similar work for two bluff bodies, there has been hardly any work on systematic investigations of the fluid force components varying with alignment angles. • Such result is extremely important for vortex-induced vibration and fatigue analysis of the cylinder. • The problem is solved numerically by the lattice Boltzmann method coupled with the immersed boundary method. The extensive results have been provided to show the nature of the fluid force and vortex contour at different alignment angles. [ABSTRACT FROM AUTHOR]

In this study, we present a parallel immersed boundary strategy that uses Nitsche's method (noted NIB) to weakly impose on a given fluid the boundary conditions associated with a solid of arbitrary shape and motion. Specific details of the software implementation, as done in the software Lethe, are discussed. We verify the NIB method and compare it with other methods in the literature on the well-established test cases of Taylor-Couette flow and von Karman vortex street. Then, we validate the NIB method through simulations of the mixing of fluid in a stirred tank, which is a process central to industries as diverse as polymer manufacturing, food processing, pharmaceutical or chemicals. Simulation results show excellent agreement with experimental data available in the literature for a large range of Reynolds numbers (▪), for baffled and unbaffled tanks with a pitched-blade turbine (PBT) impeller. Lastly, the versatility of the NIB method is demonstrated with simulations of a mixing rig with two off-centered impellers with overlapping swept volumes, a case that is either unpractical or impossible to simulate with many other techniques. The software as well as all the files that we used for the simulations are available in the public domain for ease of reproducibility. • An immersed boundary method is formulated and validated with experimental data. • The method can simulate the motion of solids of any shapes inside a viscous fluid. • The method successfully simulates impellers with overlapping swept volumes. • Software and files for the simulations are available in the public domain. [ABSTRACT FROM AUTHOR]

Embedded (or immersed) boundary methods (EBMs) for CFD and fluid-structure interaction (FSI) are attractive for aerodynamic optimization problems characterized by large shape deformations and surface topology changes. At each iteration, they eliminate the need for explicitly remeshing a computational fluid domain and avoid the pitfalls of transferring information from one CFD mesh to another. However, they are vulnerable to discrete events that compromise the smoothness of the aerodynamic objective and/or constraint functions they may compute. For this reason, the realization of EBMs for gradient-based aerodynamic shape optimization requires first their endowment with sufficient smoothness guarantees. Drawing on a recently developed EBM for the solution of compressible viscous fluid and FSI problems with such guarantees, this paper demonstrates the potential of shape-differentiable EBMs for discovering optimal aerodynamic designs featuring significant shape deformations and surface topology changes. Specifically, it highlights their advantages in terms of reliability with respect to large shape adjustments and surface topology changes, efficiency, simplicity, and reduced need for user intervention. To this end, the paper showcases the application of an advanced EBM with smoothness guarantees to wing shape, wing section, and nacelle-pylon placement optimization problems formulated for a NASA Common Research Model (CRM). • Analytical sensitivities of a differentiable embedded boundary method (EBM). • Application of an EBM to gradient-based shape optimization problems. • Realistic shape design problems dominated by large shape and topology changes. [ABSTRACT FROM AUTHOR]

A numerical strategy based on an immersed boundary method (IBM) is presented for performing high-fidelity simulation of thermal hydraulics while including Conjugate Heat Transfer (CHT). The well documented pipe flow is considered which, despite its academic nature, can be seen as a prototype of complex geometry in the sense that the computational mesh, only regular and Cartesian, is not in any way designed to fit the wall. An original strategy is proposed to impose Neumann boundary conditions in this generic situation where the wall geometry is disconnected from the mesh organization. As a first validation step, the technique is used in the context of heat transfer in pipe flow with isoflux conditions (IF). The actual order of accuracy is assessed in laminar regime and then direct numerical simulation (DNS) results are compared to turbulent data of reference, including first- and second-order one-point statistics, as well as budgets of temperature variance for a Reynolds number R e = 5300 and two Prandtl numbers P r = 0.025 , 0.71. The technique is then used to develop a versatile methodology for CHT simulations, where the coupling between fluid and solid thermal solution is performed by an immersed boundary technique that translates the information from the normal and tangential surface directions into the Cartesian grid directions. Consistent results are presented in laminar and turbulent regimes, through the check of the accuracy order for the former and the analysis of turbulent statistics for the latter, including the assessment of the discontinuity of the temperature variance dissipation across the fluid-solid interface. • Original IBM to impose Neumann BC when wall-geometry and mesh-grid are disconnected. • Method is extended to CHT, the thermal coupling being ensured by local 1D operators. • Laminar validation results in pipe include check of the accuracy order. • Turbulent pipe results include basic as well as small-scale/high-order statistics. [ABSTRACT FROM AUTHOR]

We propose an immersed boundary scheme for the numerical resolution of the Complete Electrode Model in Electrical Impedance Tomography, that we use as a main ingredient in the resolution of inverse problems in medical imaging. Such method allows to use a Cartesian mesh without accurate discretization of the boundary, which is useful in situations where the boundary is complicated and/or changing. We prove the convergence of our method, and illustrate its efficiency with two dimensional direct and inverse problems. • The resolution of the Complete Electrode Model in Electrical Impedance Tomography by immersed boundary methods is assessed. • Several equivalent formulations of the CEM are considered. • A first order finite difference Immersed Boundary Method is established. • Its efficiency is demonstrated on direct and inverse problems related to EIT, in particular the Calderon's problem. [ABSTRACT FROM AUTHOR]

We present a novel framework to deal with static and moving immersed boundaries (IB) based on volume-filtering. In this strategy, called Volume-Filtering Immersed Boundary (VFIB) method, transport equations are derived by filtering the Navier-Stokes equations and accounting for stresses at the solid-fluid interface. The result is that boundary conditions that normally apply on the solid-fluid interface are transformed into bodyforces that apply on the right-hand side of the filtered transport equations. In this method, the filter width acts as a parameter that controls the level of resolution. The IB is considered well-resolved if the filter width is much smaller than the characteristic corrugation scale of the interface. There are several innovations in this IB method. First, it sheds light on the role of the internal flow which arises when the transport equations are solved inside the IB. We show that, it is essential to separate stresses due to the external and internal fluids in order to get accurate forces, and provide a method to do so. Second, we show that the volumes associated with Lagrangian forcing points on the boundary depend on the local topology of the surface. We provide a straightforward way to compute these volumes using a triangle tessellation of the interface and the surface density function. Third, we provide an efficient procedure to compute the solid volume fraction, thus, enabling tagging interior/exterior cells. This volume fraction is also involved in the procedure to separate stresses due to the external fluid from the total stresses. Fourth, we show a path forward to extend the VFIB method to Large Eddy Simulations involving IBs. Lastly, we apply the VFIB in several numerical tests involving two- and three-dimensional static and moving IBs. We show greatly improved results compared to prior IB methods. Further, we test several filter kernels and show that, for well-resolved IBs, the choice of the kernel plays little role. • We present a new framework for immersed boundary methods free from ad-hoc fixes. • This a robust and stable method that is well suited for FSI and PR-DNS. • We derive the method rigorously by volume-filtering the Navier-Stokes equations. • We show how to get hydrodynamic stresses from resolved and subfilter stresses. • The method gives excellent results in benchmark tests with fixed and moving IBs. [ABSTRACT FROM AUTHOR]

For the thermal–fluid–structure interaction (TFSI) problems with moving boundaries, the original implicit boundary condition-enforced immersed boundary method (IBM) by Wang et al. [1] has to generate a large correlation matrix and compute its inversion at each iteration, implying that the virtual memory requirement and computational cost would grow exponentially with the number of Lagrangian points. In this work, we proposed an efficient explicit boundary condition-enforced immersed boundary method for Neumann boundary condition (NBC) to achieve high computational efficiency and maintain similar accuracy as the original implicit IBM [1] , which circumvents the needs to assemble a large correlation matrix and inverse it in the original implicit IBM [1] through second-order approximation based on the error analysis using Taylor series expansion. Most importantly, the proposed explicit IBM can efficiently solve practical physics problems with a tremendous amount of Lagrangian points involving Neumann boundary condition. The comparisons of the virtual memory and computational cost between the explicit and implicit IBMs demonstrate that the explicit boundary condition-enforced IBM is not only computational efficient, but also has memory saving performance. The proposed explicit IBM integrated with the reconstructed thermal lattice Boltzmann flux solver (RTLBFS) is validated with some classical benchmarks, and the results show that the proposed explicit IBM can successfully resolve TFSI problems with Neumann boundary condition. • An explicit boundary condition-enforced immersed boundary method is proposed. • The new explicit IBM can accurately impose Neumann boundary conditions. • The new explicit IBM is more efficient than the conventional implicit IBM. • The new explicit IBM can preserve second-order accuracy. • The new explicit IBM can efficiently solve 3D TFSI problems with moving boundaries. [ABSTRACT FROM AUTHOR]

The Finite Volume method with Exact two-material Riemann Problems (FIVER) is both a computational framework for multi-material flows characterized by large density jumps, and an Embedded Boundary Method (EBM) for computational fluid dynamics and highly nonlinear Fluid–Structure Interaction (FSI) problems. This paper deals with the EBM aspect of FIVER. For FSI problems, this EBM has already demonstrated the ability to address viscous effects along wall boundaries, and large deformations and topological changes of such boundaries. However, like for most EBMs – also known as immersed boundary methods – the performance of FIVER in the vicinity of a wall boundary can be sensitive with respect to the position and orientation of this boundary relative to the embedding mesh. This is mainly due to ill-conditioning issues that arise when an embedded interface becomes too close to a node of the embedding mesh, which may lead to spurious oscillations in the computed solution gradients at the wall boundary. This paper resolves these issues by introducing an alternative definition of the active/inactive status of a mesh node that leads to the removal of all sources of potential ill-conditioning from all spatial approximations performed by FIVER in the vicinity of a fluid–structure interface. It also makes two additional contributions. The first one is a new procedure for constructing the fluid–structure half Riemann problem underlying the semi-discretization by FIVER of the convective fluxes. This procedure eliminates one extrapolation from the conventional treatment of the wall boundary conditions and replaces it by an interpolation, which improves robustness. The second contribution is a post-processing algorithm for computing quantities of interest at the wall that achieves smoothness in the computed solution and its gradients. Lessons learned from these enhancements and contributions that are triggered by the new definition of the status of a mesh node are then generalized and exploited to eliminate from the original version of the FIVER method its sensitivities with respect to both of the position and orientation of the wall boundary relative to the embedding mesh, while maintaining the original definition of the status of a mesh node. This leads to a family of second-generation FIVER methods whose performance is illustrated in this paper for several flow and FSI problems. These include a challenging flow problem over a bird wing characterized by a feather-induced surface roughness, and a complex flexible flapping wing problem for which experimental data is available. [ABSTRACT FROM AUTHOR]

We present an analytical study of discretization stencils for the Poisson problem and the incompressible Navier–Stokes problem when used with some direct forcing immersed boundary methods. This study uses, but is not limited to, second-order discretization and Ghost-Cell Finite-Difference methods. We show that the stencil size increases with the aspect ratio of rectangular cells, which is undesirable as it breaks assumptions of some linear system solvers. To circumvent this drawback, a modification of the Ghost-Cell Finite-Difference methods is proposed to reduce the size of the discretization stencil to the one observed for square cells, i.e. with an aspect ratio equal to one. Numerical results validate this proposed method in terms of accuracy and convergence, for the Poisson problem and both Dirichlet and Neumann boundary conditions. An improvement on error levels is also observed. In addition, we show that the application of the chosen Ghost-Cell Finite-Difference methods to the Navier–Stokes problem, discretized by a pressure-correction method, requires an additional interpolation step. This extra step is implemented and validated through well known test cases of the Navier–Stokes equations. [ABSTRACT FROM AUTHOR]

We present a dimensionally split method for solving hyperbolic conservation laws on Cartesian cut cell meshes. The approach combines local geometric and wave speed information to determine a novel stabilised cut cell flux, and we provide a full description of its three-dimensional implementation in the dimensionally split framework of Klein et al. [1] . The convergence and stability of the method are proved for the one-dimensional linear advection equation, while its multi-dimensional numerical performance is investigated through the computation of solutions to a number of test problems for the linear advection and Euler equations. When compared to the cut cell flux of Klein et al., it was found that the new flux alleviates the problem of oscillatory boundary solutions produced by the former at higher Courant numbers, and also enables the computation of more accurate solutions near stagnation points. Being dimensionally split, the method is simple to implement and extends readily to multiple dimensions. [ABSTRACT FROM AUTHOR]

Type 2 diabetes mellitus (DM2) is frequently accompanied by microcirculation complications, including structural and functional alterations, which may have serious effects on substance exchanges between blood and interstitial tissue and the health of organs. In this paper, we aim to study the influence of microcirculation alterations in DM2 patients on fluid and oxygen exchanges through a model analysis. A fluid flow and oxygen transport model were developed by considering the interplay between blood in capillary network and interstitial tissue. The two regions were separately represented by 1D network model and 3D volume model, and the immersed boundary method (IBM) was adopted to solve fluid and mass transfer between these two regions. By using the model, the steady flow field and the distributions of oxygen in capillary network and surrounding tissue were firstly simulated. In the interstitial volume, fluid pressure and oxygen tension decreased with the increase of distance from the network; in the network, oxygen tension in blood plasma dropped from 100 mm Hg at the entrance to about 40 mm Hg at the exit. We further tested several structural and functional disorders related to diabetic pathological conditions. Simulated results show that the impaired connectivity of the network could result in poor robustness in maintaining blood flow and perfused surface; under high fluid permeability conditions of capillary walls, the pressure gradient was much larger around the capillary bed, and this alteration led to a saturation level of the interstitial pressure when lymphatic flow drainage can't work effectively; the variations in network connectivity and permeability of capillary wall also had unfavorable influence on oxygen distributions in interstitial tissue. In addition, when the oxygen releasing capacity of hemoglobin was confined by glycosylated hemoglobin (HbA1) in the case of diabetes, the plasma could not be complemented with adequate oxygen and thus the hypoxic tissue range will be extended. This study illustrates that when microcirculation disturbances, including the structure of capillary network, the wall osmosis property and the capacity of blood binding oxygen occur in DM2, some negative impacts are raised on microvascular hemodynamics and metabolism circumstance of interstitial tissue. [ABSTRACT FROM AUTHOR]

In this study, a multi-moment finite volume method (FVM) based on block-structured adaptive Cartesian mesh is proposed for simulating incompressible flows. A conservative interpolation scheme following the idea of the constrained interpolation profile (CIP) method is proposed for the prolongation operation of the newly created mesh. A sharp immersed boundary (IB) method is used to model the immersed rigid body. A moving least squares (MLS) interpolation approach is applied for reconstruction of the velocity field around the solid surface. An efficient method for discretization of Laplacian operators on adaptive meshes is proposed. Numerical simulations on several test cases are carried out for validation of the proposed method. For the case of viscous flow past an impulsively started cylinder ( Re = 3000 , 9500 ), the computed surface vorticity coincides with the result of the body-fitted method. For the case of a fast pitching NACA 0015 airfoil at moderate Reynolds numbers ( Re = 10000 , 45000 ), the predicted drag coefficient ( C D ) and lift coefficient ( C L ) agree well with other numerical or experimental results. For 2D and 3D simulations of viscous flow past a pitching plate with prescribed motions ( Re = 5000 , 40000 ), the predicted C D , C L and C M (moment coefficient) are in good agreement with those obtained by other numerical methods. [ABSTRACT FROM AUTHOR]

We present a weak-coupling approach for fluid–structure interaction with low density ratio ( ρ ) of solid to fluid. For accurate and stable solutions, we introduce predictors, an explicit two-step method and the implicit Euler method, to obtain provisional velocity and position of fluid–structure interface at each time step, respectively. The incompressible Navier–Stokes equations, together with these provisional velocity and position at the fluid–structure interface, are solved in an Eulerian coordinate using an immersed-boundary finite-volume method on a staggered mesh. The dynamic equation of an elastic solid-body motion, together with the hydrodynamic force at the provisional position of the interface, is solved in a Lagrangian coordinate using a finite element method. Each governing equation for fluid and structure is implicitly solved using second-order time integrators. The overall second-order temporal accuracy is preserved even with the use of lower-order predictors. A linear stability analysis is also conducted for an ideal case to find the optimal explicit two-step method that provides stable solutions down to the lowest density ratio. With the present weak coupling, three different fluid–structure interaction problems were simulated: flows around an elastically mounted rigid circular cylinder, an elastic beam attached to the base of a stationary circular cylinder, and a flexible plate, respectively. The lowest density ratios providing stable solutions are searched for the first two problems and they are much lower than 1 ( ρ min = 0.21 and 0.31, respectively). The simulation results agree well with those from strong coupling suggested here and also from previous numerical and experimental studies, indicating the efficiency and accuracy of the present weak coupling. [ABSTRACT FROM AUTHOR]

A high-order adaptive Cartesian cut-cell method, developed in the past by the authors [1] for simulation of compressible viscous flow over static embedded boundaries, is now extended for reacting flow simulations over moving interfaces. The main difficulty related to simulation of moving boundary problems using immersed boundary techniques is the loss of conservation of mass, momentum and energy during the transition of numerical grid cells from solid to fluid and vice versa. Gas phase reactions near solid boundaries can produce huge source terms to the governing equations, which if not properly treated for moving boundaries, can result in inaccuracies in numerical predictions. The small cell clustering algorithm proposed in our previous work is now extended to handle moving boundaries enforcing strict conservation. In addition, the cell clustering algorithm also preserves the smoothness of solution near moving surfaces. A second order Runge–Kutta scheme where the boundaries are allowed to change during the sub-time steps is employed. This scheme improves the time accuracy of the calculations when the body motion is driven by hydrodynamic forces. Simple one dimensional reacting and non-reacting studies of moving piston are first performed in order to demonstrate the accuracy of the proposed method. Results are then reported for flow past moving cylinders at subsonic and supersonic velocities in a viscous compressible flow and are compared with theoretical and previously available experimental data. The ability of the scheme to handle deforming boundaries and interaction of hydrodynamic forces with rigid body motion is demonstrated using different test cases. Finally, the method is applied to investigate the detonation initiation and stabilization mechanisms on a cylinder and a sphere, when they are launched into a detonable mixture. The effect of the filling pressure on the detonation stabilization mechanisms over a hyper-velocity sphere launched into a hydrogen–oxygen–argon mixture is studied and a qualitative comparison of the results with the experimental data are made. Results indicate that the current method is able to correctly reproduce the different regimes of combustion observed in the experiments. Through the various examples it is demonstrated that our method is robust and accurate for simulation of compressible viscous reacting flow problems with moving/deforming boundaries. [ABSTRACT FROM AUTHOR]

Many biological examples of fluid–structure interaction, including the transit of red blood cells through the narrow slits in the spleen and the intracellular trafficking of vesicles into dendritic spines, involve the near-contact of elastic structures separated by thin layers of fluid. Motivated by such problems, we introduce an immersed boundary method that uses elements of lubrication theory to resolve thin fluid layers between immersed boundaries. We demonstrate 2nd-order accurate convergence for simple two-dimensional flows with known exact solutions to showcase the increased accuracy of this method compared to the standard immersed boundary method. Motivated by the phenomenon of wall-induced migration, we apply the lubricated immersed boundary method to simulate an elastic vesicle near a wall in shear flow. We also simulate the dynamics of a vesicle traveling through a narrow channel and observe the ability of the lubricated method to capture the vesicle motion on relatively coarse fluid grids. [ABSTRACT FROM AUTHOR]

We present a robust sharp-interface immersed boundary method for numerically studying high speed flows of compressible and viscous fluids interacting with arbitrarily shaped either stationary or moving rigid solids. The Navier–Stokes equations are discretized on a rectangular Cartesian grid based on a low-diffusion flux splitting method for inviscid fluxes and conservative high-order central-difference schemes for the viscous components. Discontinuities such as those introduced by shock waves and contact surfaces are captured by using a high-resolution weighted essentially non-oscillatory (WENO) scheme. Ghost cells in the vicinity of the fluid–solid interface are introduced to satisfy boundary conditions on the interface. Values of variables in the ghost cells are found by using a constrained moving least squares method (CMLS) that eliminates numerical instabilities encountered in the conventional MLS formulation. The solution of the fluid flow and the solid motion equations is advanced in time by using the third-order Runge–Kutta and the implicit Newmark integration schemes, respectively. The performance of the proposed method has been assessed by computing results for the following four problems: shock-boundary layer interaction, supersonic viscous flows past a rigid cylinder, moving piston in a shock tube and lifting off from a flat surface of circular, rectangular and elliptic cylinders triggered by shock waves, and comparing computed results with those available in the literature. [ABSTRACT FROM AUTHOR]

Lagrangian, direct-forcing, immersed boundary (IB) methods have been receiving increased attention due to their robustness in complex fluid-structure interaction problems. They are very sensitive, however, on the selection of the Lagrangian grid, which is typically used to define a solid or flexible body immersed in a fluid flow. In the present work we propose a cost-efficient solution to this problem without compromising accuracy. Central to our approach is the use of isoparametric mapping to bridge the relative resolution requirements of Lagrangian IB, and Eulerian grids. With this approach, the density of surface Lagrangian markers, which is essential to properly enforce boundary conditions, is adapted dynamically based on the characteristics of the underlying Eulerian grid. The markers are not stored and the Lagrangian data-structure is not modified. The proposed scheme is implemented in the framework of a moving least squares reconstruction formulation, but it can be adapted to any Lagrangian, direct-forcing formulation. The accuracy and robustness of the approach is demonstrated in a variety of test cases of increasing complexity. [ABSTRACT FROM AUTHOR]

Osmotic forces and solute diffusion are increasingly seen as playing a fundamental role in cell movement. Here, we present a numerical method that allows for studying the interplay between diffusive, osmotic and mechanical effects. An osmotically active solute obeys a advection–diffusion equation in a region demarcated by a deformable membrane. The interfacial membrane allows transmembrane water flow which is determined by osmotic and mechanical pressure differences across the membrane. The numerical method is based on an immersed boundary method for fluid–structure interaction and a Cartesian grid embedded boundary method for the solute. We demonstrate our numerical algorithm with the test case of an osmotic engine, a recently proposed mechanism for cell propulsion. [ABSTRACT FROM AUTHOR]

In this paper, we propose a hybrid model to compute the capillary force acting on moving solid objects, and combine it with the diffuse-interface immersed-boundary method in Liu and Ding (2015) [18] to simulate fluid–structure interaction (FSI) involving dynamic wetting. Dynamic wetting is very important in the dynamic interaction between fluid–fluid interfaces and small moving objects. Numerical simulations of these flow problems require accurate computation of the capillary force acting on the structure, which depends on the instantaneous position of and the effective surface tension at the moving contact line. In order to achieve this, we use the diffuse-interface immersed-boundary method to simulate the dynamic wetting on moving objects, and propose a hybrid model to compute the effective surface tension at the contact line. Specifically, a diffuse interface model is used for the interface profile out of equilibrium, e.g. at the onset of formation or detachment of contact lines, and a sharp interface model is used for the interface profile at equilibrium. The performance of the method is examined by a variety of numerical experiments. We simulate the sinking of a circular cylinder due to gravity, and study the capillarity-dominated impact dynamics of a solid sphere on a water pool. In both cases the numerical results are quantitatively compared against the experimental data, and good agreements have been achieved. The momentum conservation of the system is carefully checked by studying head-on collision between a drop and a solid sphere. Finally, we apply the method to the self-assembly process of multiple floating cylinders on water surface. [ABSTRACT FROM AUTHOR]

In this work, we extend our previous esophageal transport model using an immersed boundary (IB) method with discrete fiber-based structural model, to one using a continuum mechanics-based model that is approximated based on finite elements (IB-FE). To deal with the leakage of flow when the Lagrangian mesh becomes coarser than the fluid mesh, we employ adaptive interaction quadrature points to deal with Lagrangian–Eulerian interaction equations based on a previous work (Griffith and Luo [1] ). In particular, we introduce a new anisotropic adaptive interaction quadrature rule. The new rule permits us to vary the interaction quadrature points not only at each time-step and element but also at different orientations per element. This helps to avoid the leakage issue without sacrificing the computational efficiency and accuracy in dealing with the interaction equations. For the material model, we extend our previous fiber-based model to a continuum-based model. We present formulations for general fiber-reinforced material models in the IB-FE framework. The new material model can handle non-linear elasticity and fiber-matrix interactions, and thus permits us to consider more realistic material behavior of biological tissues. To validate our method, we first study a case in which a three-dimensional short tube is dilated. Results on the pressure-displacement relationship and the stress distribution matches very well with those obtained from the implicit FE method. We remark that in our IB-FE case, the three-dimensional tube undergoes a very large deformation and the Lagrangian mesh-size becomes about 6 times of Eulerian mesh-size in the circumferential orientation. To validate the performance of the method in handling fiber-matrix material models, we perform a second study on dilating a long fiber-reinforced tube. Errors are small when we compare numerical solutions with analytical solutions. The technique is then applied to the problem of esophageal transport. We use two fiber-reinforced models for the esophageal tissue: a bi-linear model and an exponential model. We present three cases on esophageal transport that differ in the material model and the muscle fiber architecture. The overall transport features are consistent with those observed from the previous model. We remark that the continuum-based model can handle more realistic and complicated material behavior. This is demonstrated in our third case where a spatially varying fiber architecture is included based on experimental study. We find that this unique muscle fiber architecture could generate a so-called pressure transition zone, which is a luminal pressure pattern that is of clinical interest. This suggests an important role of muscle fiber architecture in esophageal transport. [ABSTRACT FROM AUTHOR]

The Immersed Boundary (IB) method is a mathematical framework for constructing robust numerical methods to study fluid–structure interaction in problems involving an elastic structure immersed in a viscous fluid. The IB formulation uses an Eulerian representation of the fluid and a Lagrangian representation of the structure. The Lagrangian and Eulerian frames are coupled by integral transforms with delta function kernels. The discretized IB equations use approximations to these transforms with regularized delta function kernels to interpolate the fluid velocity to the structure, and to spread structural forces to the fluid. It is well-known that the conventional IB method can suffer from poor volume conservation since the interpolated Lagrangian velocity field is not generally divergence-free, and so this can cause spurious volume changes. In practice, the lack of volume conservation is especially pronounced for cases where there are large pressure differences across thin structural boundaries. The aim of this paper is to greatly reduce the volume error of the IB method by introducing velocity-interpolation and force-spreading schemes with the properties that the interpolated velocity field in which the structure moves is at least C 1 and satisfies a continuous divergence-free condition, and that the force-spreading operator is the adjoint of the velocity-interpolation operator. We confirm through numerical experiments in two and three spatial dimensions that this new IB method is able to achieve substantial improvement in volume conservation compared to other existing IB methods, at the expense of a modest increase in the computational cost. Further, the new method provides smoother Lagrangian forces (tractions) than traditional IB methods. The method presented here is restricted to periodic computational domains. Its generalization to non-periodic domains is important future work. [ABSTRACT FROM AUTHOR]

We present a moving control volume (CV) approach to computing hydrodynamic forces and torques on complex geometries. The method requires surface and volumetric integrals over a simple and regular Cartesian box that moves with an arbitrary velocity to enclose the body at all times. The moving box is aligned with Cartesian grid faces, which makes the integral evaluation straightforward in an immersed boundary (IB) framework. Discontinuous and noisy derivatives of velocity and pressure at the fluid–structure interface are avoided and far-field (smooth) velocity and pressure information is used. We re-visit the approach to compute hydrodynamic forces and torques through force/torque balance equations in a Lagrangian frame that some of us took in a prior work (Bhalla et al., 2013 [13] ). We prove the equivalence of the two approaches for IB methods, thanks to the use of Peskin's delta functions. Both approaches are able to suppress spurious force oscillations and are in excellent agreement, as expected theoretically. Test cases ranging from Stokes to high Reynolds number regimes are considered. We discuss regridding issues for the moving CV method in an adaptive mesh refinement (AMR) context. The proposed moving CV method is not limited to a specific IB method and can also be used, for example, with embedded boundary methods. [ABSTRACT FROM AUTHOR]