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In this paper, the computational examination is carried out on the heat generation, Soret and Dufour’s influence on the unsteady MHD convection flow of an incompressible viscous fluid with chemical reaction. It is due to the exponentially accelerated vertical porous plate embedded in a permeable medium with ramped wall temperature together with surface concentration and also with thermal radiation impacts. The basic governing set of the equations of the fluid dynamics to the flow is converted into nondimensional form by inserting suitable nondimensional parameters and variables. In addition, the resultant equations are solved computationally with the efficient Crank–Nicolsons implicit finite difference methodology. The influences for several imperative substantial parameters for the model on the velocity, temperature and concentration for the fluids, the skin friction coefficient, Nusselt and Sherwood number for together thermal situations have been explored with the help of graphical profiles and tabular forms. It is found that, the increasing quantities of the Dufour, temperature generation and thermal radiation parameters, the fluid temperature as well as velocity enhances. Similarly, it is noted that an escalating Soret parameter causes the fluid’s velocity and concentration whereas the chemical reaction parameter notifies reversal outputs. [ABSTRACT FROM AUTHOR]

A few basic, intuitive, properties of the Navier–Stokes system of equations for incompressible fluid flows are discussed in this paper. We present a rephrased interpretation of the Navier–Stokes equation in a space having an arbitrary number of dimensions. We then derive spatially periodic solutions for the velocity and pressure fields that span an unbounded domain in three and four dimensions, given a smooth solenoidal initial velocity vector field. In these solutions all velocity components depend non-trivially on all coordinate directions. [ABSTRACT FROM AUTHOR]

Microscopic active droplets are able to swim autonomously in viscous flows. This puzzling feature stems from solute exchanges with the surrounding fluid via surface reactions or their spontaneous solubilization and from the interfacial flows resulting from these solutes' gradients. Contrary to asymmetric active colloids, these isotropic droplets swim spontaneously by exploiting the nonlinear coupling of solute transport with self-generated Marangoni flows; such coupling is also responsible for secondary transitions to more complex individual and collective dynamics. Thanks to their simple design and their sensitivity to physico-chemical signals, these droplets are fascinating to physicists, chemists, biologists, and fluid dynamicists alike in analyzing viscous self-propulsion and collective dynamics in active-matter systems, developing synthetic cellular models, or performing targeted biomedical or engineering applications. I review here the most recent and significant developments of this rapidly growing field, focusing on the mathematical and physical modeling of these intriguing droplets, together with their experimental design and characterization. [ABSTRACT FROM AUTHOR]

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A rotational version of the fluid-mechanical sewing machine (FMSM) is investigated experimentally. A thin thread of silicon oil was dispensed at a constant flow rate Q from a height H and fell on a table rotating at an angular speed ω , at a distance R from the axis. In all experimental runs, the values of Q and H were kept constant while the radius R was changed manually after each full rotation. Preliminary results show that the usual stitching patterns ensue as the local linear speed V = ω R approaches the critical transition speeds seen in the FMSM scenario but with subtle asymmetries introduced by rotational (centrifugal) effects. In some instances, arcs and loops of the traces were noticeably more pronounced when directed outward compared to those pointing toward the axis of rotation. Moreover, we observed stitching patterns not reported before. Overall, the symmetry-breaking features, while clearly visible, were rather subtle. Their morphological characteristics, such as differences in local curvature of traces relative to those in FMSM, are estimated to be below 10% in most cases. [ABSTRACT FROM AUTHOR]

The effects of roughness parameters, including height, diameter, and spacing of the cylindrical roughness elements, on turbulent transition are investigated in a three-dimensional boundary layer using direct numerical simulation. There are two types of transition process, classified as gradual and forced. The former is caused by a linear development of crossflow vortices and their secondary instability, while the latter is an immediate breakdown to turbulence behind the roughness without any crossflow vortex. These processes are only demarcated by the roughness height. The diameter and the spacing affect the initial creation processes of the crossflow vortex as well as the onset of the secondary instability in the gradual transition. With a fixed roughness volume, the greater height induces larger initial disturbances and causes earlier transition than a larger diameter. The aforementioned observations apply when the most unstable crossflow mode is induced. When the unstable mode is absent or is secondarily induced, the disturbance decays or the transition point shifts downstream. Therefore, when considering the critical parameter between the gradual and forced transitions, only the height is crucial. However, for a gradual transition, roughness parameters affect the transition point and we should consider the flow alternation caused by the roughness. [ABSTRACT FROM AUTHOR]

This paper presents a Lagrangian vortex method combined with iterative Brinkman penalization for the simulation of incompressible flow past a complex geometry. In the proposed algorithm, particle and penalization domains are separately introduced. The particle domain is for the computation of particle convection and diffusion, while the penalization domain is the enforcement of the wall boundary conditions. In iterative Brinkman penalization, the no-slip boundary condition is enforced by applying penalization force in multiple times within each time step. This enables large time step size reducing computational cost and maintains the capability in handling complex geometries. The method is validated for benchmark problems such as an impulsively started flow past a circular cylinder, normal to a flat plate, and a symmetric airfoil at Reynolds numbers ranging from 550 to 1000. The vorticity and streamline contours, drag, and lift coefficients show a good agreement with those reported in literature. [ABSTRACT FROM AUTHOR]

Two-dimensional dynamics of the wake in transitional flow around a circular cylinder is studied using weakly compressible smoothed particle hydrodynamics scheme up to 10 cylinder diameters downstream at a Reynolds number of 4000. The main objectives of this study are to evaluate the capability of SPH-LES and artificial viscosity in capturing flow activity as well as to test the performance of these formulations and background pressure coupling against the so-called tensile instability and to understand the effect of this instability in terms of mean integral quantities, first-order statistics and frequency spectra. It is observed that the effect of viscous formulation on flow dynamics becomes significant between four-and-seven diameters downstream of the cylinder. Background pressure coupling shifts the onset of transition about two diameters upstream by creating stiffer density field; however, it results in more energetic smaller scale activity. [ABSTRACT FROM AUTHOR]

In this paper, we resolve the ever‐present confusion over the Quadratic Upwind Interpolation for Convective Kinematics (QUICK) scheme: it is a second‐order scheme or a third‐order scheme. The QUICK scheme, as proposed in the original reference (B. P. Leonard, Comput. Methods. Appl. Mech. Eng., 19, (1979), 59‐98), is a third‐order (not second‐order) finite‐volume scheme for the integral form of a general nonlinear conservation law with point‐valued solutions stored at cell centers as numerical solutions. Third‐order accuracy is proved by a careful and detailed truncation error analysis and demonstrated by a series of thorough numerical tests. The QUICK scheme requires a careful spatial discretization of a time derivative to preserve third‐order accuracy for unsteady problems. Two techniques are discussed, including the QUICKEST scheme of Leonard. Discussions are given on how the QUICK scheme is mistakenly found to be second‐order accurate. This paper is intended to serve as a reference to clarify any confusion about third‐order accuracy of the QUICK scheme and also as the basis for clarifying economical high‐order unstructured‐grid schemes as we will discuss in a subsequent paper. [ABSTRACT FROM AUTHOR]

In this short note, we introduce a flexible explicit gradient method for efficient and robust unstructured-grid computations. As shown, the method serves as a memory-efficient alternative to the multiple least-squares gradients needed by conflicting requirements for inviscid, viscous, and turbulence-model source terms (e.g., vorticity), in practical computational-fluid-dynamics solvers. The flexible method computes the gradient of a numerical solution in a cell by averaging the face gradients defined by the alpha-damped formula with a parameterαg based on a single set of least-squares gradients. We show that a small αggives less-accurate gradients similar to unweighted least-squares gradients, and a large αgproduces accurate gradients similar to weighted least-squares gradients. Therefore, it allows us to obtain two types of gradients by changing the value of αg without storing more than one set of least-squares coefficients. Moreover, the method yields fourth-order accurate gradients with αg = 10/3 on a regular grid. The method is demonstrated for two-dimensional inviscid and viscous flows on unstructured grids. [ABSTRACT FROM AUTHOR]

A spectrally accurate and very efficient algorithm suitable for prediction of pressure losses in heated grooved channels has been developed. Heating and topography patterns are used to create spatial flow modulations resulting in a pattern interaction problem. Search for combinations of patterns resulting in the reduction of pressure losses requires development of a very accurate and efficient algorithm. The proposed algorithm uses a combination of the Fourier expansions in the horizontal directions and the Chebyshev expansions in the vertical direction to provide a very good resolution of the near wall regions. The immersed boundary conditions (IBC) method is used to enforce flow boundary conditions at the geometrically irregular boundaries. The resulting gridless discretization can be easily adapted to handle a wide range of topography patterns. Various tests demonstrate that the algorithm delivers spectral accuracy and can provide machine level accuracy. Comparisons with the standard open‐source codes based either on the finite volume or on the spectral element discretization demonstrate several orders of magnitude better efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

A rotational version of the fluid-mechanical sewing machine (FMSM) is investigated experimentally. A thin thread of silicon oil was dispensed at a constant flow rate Q from a height H and fell on a table rotating at an angular speed ω, at a distance R from the axis. In all experimental runs, the values of Q and H were kept constant while the radius R was changed manually after each full rotation. Preliminary results show that the usual stitching patterns ensue as the local linear speed V=ωR approaches the critical transition speeds seen in the FMSM scenario but with subtle asymmetries introduced by rotational (centrifugal) effects. In some instances, arcs and loops of the traces were noticeably more pronounced when directed outward compared to those pointing toward the axis of rotation. Moreover, we observed stitching patterns not reported before. Overall, the symmetry-breaking features, while clearly visible, were rather subtle. Their morphological characteristics, such as differences in local curvature of traces relative to those in FMSM, are estimated to be below 10% in most cases.

A Lagrangian radial basis function‐based particle hydrodynamics method (RBFPH) is proposed. In RBFPH method, the differential quadrature technique is combined with radial basis function (RBF) to obtain the meshless high‐dimensional derivative approximations for randomly distributed particles; a particular solution of RBF is chosen to ensure the positive definite of the interpolating matrix. Like the conventional RBF, RBFPH has the advantages of simple form, isotropy and high accuracy, and is suitable for numerical calculation. Moreover, all particles in RBFPH can move with the fluid, so RBFPH may conveniently compute complex flows with the moving boundary. A series of numerical examples are conducted to test the accuracy of RBFPH, and the results show the RBFPH has second‐order convergence, which shows its great advantage in terms of accuracy. The RBFPH is validated by its application to the simulations of Taylor–Green flow, lid driven shear cavity flows, stretching of a free‐surface circular fluid patch and flows around a cylinder. Excellent agreements with analytical solutions and reference results indicate that the proposed method has a promising application in simulating viscous flows with the moving boundary, large deformation, and free surface. [ABSTRACT FROM AUTHOR]

This article is a rebuttal to the claim found in the literature that the monotonic upstream‐centered scheme for conservation laws (MUSCL) cannot be third‐order accurate for nonlinear conservation laws. We provide a rigorous proof for third‐order accuracy of the MUSCL scheme based on a careful and detailed truncation error analysis. Throughout the analysis, the distinction between the cell average and the point value will be strictly made for the numerical solution as well as for the target operator. It is shown that the average of the solutions reconstructed at a face by Van Leer's κ‐scheme recovers a cubic solution exactly with κ=1/3, the same is true for the average of the nonlinear fluxes evaluated by the reconstructed solutions, and a dissipation term is already sufficiently small with a third‐order truncation error. Finally, noting that the target spatial operator is a cell‐averaged flux derivative, we prove that the leading truncation error of the MUSCL finite‐volume scheme is third‐order with κ=1/3. The importance of the diffusion scheme is also discussed: third‐order accuracy will be lost when the third‐order MUSLC scheme is used with an incompatible fourth‐order diffusion scheme for convection‐diffusion problems. Third‐order accuracy is verified by thorough numerical experiments for both steady and unsteady problems. This article is intended to serve as a reference to clarify confusions about third‐order accuracy of the MUSCL scheme, as a guide to correctly analyze and verify the MUSCL scheme for nonlinear equations, and eventually as the basis for clarifying high‐order unstructured‐grid schemes in a subsequent article. [ABSTRACT FROM AUTHOR]

The steady lateral spreading of a free-surface viscous flow down an inclined plane around a vertex from which the channel width increases linearly with downstream distance is investigated analytically, numerically and experimentally. From the vertex the channel wall opens by an angle α to the downslope direction and the viscous fluid spreads laterally along it before detaching. The motion is modelled using lubrication theory and the distance at which the flow detaches is computed as a function of α using analytical and numerical methods. Far downslope after detachment, it is shown that the motion is accurately modelled in terms of a similarity solution. Moreover, the detachment point is well approximated by a simple expression for a broad range of opening angles. The results are corroborated through a series of laboratory experiments and the implication for the design of barriers to divert lava flows are discussed. This article is part of the theme issue 'Stokes at 200 (Part 1)'. [ABSTRACT FROM AUTHOR]

This work presents a reduced order modeling technique built on a high fidelity embedded mesh finite element method. Such methods, and in particular the CutFEM method, are attractive in the generation of projection-based reduced order models thanks to their capabilities to seamlessly handle large deformations of parametrized domains and in general to handle topological changes. The combination of embedded methods and reduced order models allows us to obtain fast evaluation of parametrized problems, avoiding remeshing as well as the reference domain formulation, often used in the reduced order modeling for boundary fitted finite element formulations. The resulting novel methodology is presented on linear elliptic and Stokes problems, together with several test cases to assess its capability. The role of a proper extension and transport of embedded solutions to a common background is analyzed in detail. [ABSTRACT FROM AUTHOR]

Infinite-dimensional space of axisymmetric exact solutions to the Navier–Stokes equations with time-dependent viscosity ν (t) $\nu(t)$ is constructed. Inner transformations of the exact solutions are defined that produce an infinite sequence of new solutions from each known one. The solutions are analytic in the whole space ℝ3 and are described by elementary functions. The bifurcations of the instantaneous (for t = t 0 $t={t_{0}}$) phase portraits of the viscous fluid flows are studied for the new exact solutions. Backlund transforms between the axisymmetric Helmholtz equation and a linear case of the Grad–Shafranov equation are derived. [ABSTRACT FROM AUTHOR]

Aerodynamics of an owl-like wing model at low Reynolds numbers (Re = O(104-5)) are investigated using largeeddy simulations with high-resolution computational schemes. The airfoil shape of the owl-like wing model is constructed based on a cross-sectional geometry of the owl wing at 40% wingspan from the root. The chord-based Re ranges from 1.0 © 104 to 5.0 © 104 and the angle of attack (¡) varies from 0 to 14 deg. The time-averaged lift (Cl) and drag coefficients computed are in reasonable agreement with the results of force measurement. The results computed clarify a nonlinear change in the Cl curve slope, which is due to an increase in the suction peaks in conjunction with the change in type of separation, the formation of a laminar separation bubble (LSB), and pressure recovery on the pressure side. The generation of the LSB on the suction and/or pressure sides at the Re of 2.3 © 104 and 4.6 © 104 are seen, while reattachments are observed only on the pressure side at the Re of 1.0 © 104 due to the camber of the wing. Furthermore, the owl-like wing model demonstrates favorable aerodynamic performance in terms of a maximum lift-to-drag ratio in comparison with several airfoils at the Re range considered. This is due to the strong suction peaks and distribution of surface pressure on the pressure side. It is emphasized that the concave lower surface enhances the time-averaged aerodynamic performance at all of the ¡ even though the LSB is generated and fluctuation in lift history is induced at low ¡. [ABSTRACT FROM AUTHOR]

• A bubble transported by a highly viscous liquid takes a wide variety of shapes. • The bubble elongates in the direction of the flow upstream of the orifice. • Downstream of the orifice, the bubble contracts in the direction of the flow. • Bubbles contracted in the flow direction take 'crescent-moon' shapes. • Shape well-predicted by theory that assumes deformation follows the bulk flow field. Experiments and theory concern the behaviour of a small bubble carried through an orifice by a very viscous liquid. The liquid was polybutene oil, of viscosity about 70 Pa s, i.e. 70,000 times that of water. The Reynolds number of the flow is substantially less than one, hence the flow pattern is approximately radial flowing into, and away from, the orifice. These flow patterns have profound effects on the shape of an entrained bubble. On the upstream side, the acceleration of the liquid, as it approaches the orifice, causes elongation of the bubble since the front of the bubble moves faster than the back. On the downstream side, the reverse occurs: the back of the bubble moves fast than the front. Thus the height of the bubble diminishes as it moves away from the orifice, leading to the formation of a 'crescent-moon' shape. The shape of these bubbles can be predicted by considering the motion of a droplet of the same liquid replacing the bubble: the resulting geometric theory gives good predictions of bubble deformation approaching the orifice and of 'crescent-moon' formation downstream of the orifice. [ABSTRACT FROM AUTHOR]

In a seminal paper published in 1951, Taylor studied the interactions between a viscous fluid and an immersed flat sheet which is subjected to a travelling wave of transversal displacement. The net reaction of the fluid over the sheet turned out to be a force in the direction of the wave phase-speed. This effect is a key mechanism for the swimming of micro-organisms in viscous fluids. Here, we study the interaction between a viscous fluid and a special class of nonlinear morphing shells. We consider pre-stressed shells showing a onedimensional set of neutrally stable equilibria with almost cylindrical configurations. Their shape can be effectively controlled through embedded active materials, generating a large-amplitude shape-wave associated with precession of the axis of maximal curvature. We show that this shape-wave constitutes the rotational analogue of a Taylor's sheet, where the translational swimming velocity is replaced by an angular velocity. Despite the net force acting on the shell vanishes, the resultant torque does not. A similar mechanism can be used to manoeuver in viscous fluids. [ABSTRACT FROM AUTHOR]

This study presents an extension of a previous study (On an Exact Step Length in Gradient-Based Aerodynamic Shape Optimization) to viscous transonic flows. In this work, we showed that the same procedure to derive an explicit expression for an exact step length βexact in a gradient-based optimization method for inviscid transonic flows can be employed for viscous transonic flows. The extended numerical method was evaluated for the viscous flows over the transonic RAE 2822 airfoil at two common flow conditions in the transonic regime. To do so, the RAE 2822 airfoil was reconstructed by a Bezier curve of degree 16. The numerical solution of the transonic turbulent flow over the airfoil was performed using the solver ANSYS Fluent (using the Spalart–Allmaras turbulence model). Using the proposed step length, a gradient-based optimization method was employed to minimize the drag-to-lift ratio of the airfoil. The gradient of the objective function with respect to design variables was calculated by the finite-difference method. Efficiency and accuracy of the proposed method were investigated through two test cases.

This paper presents the analysis of the unsteady flows past stationary airfoils equipped with Gurney flaps at low Reynolds numbers, aiming to study the unsteady behavior of the aerodynamic coefficients due to the flow separations occurring at these Reynolds numbers. The Gurney flaps are simple but very efficient lift-increasing devices, which due to their mechanical simplicity are of particular interest for the small size micro-air-vehicles (MAV) flying at low speed and very low Reynolds number. The unsteady aerodynamic analysis is performed with an efficient time-accurate numerical method developed for the solution of the Navier-Stokes equations at low Reynolds numbers, which is second-order-accurate in time and space. The paper presents solutions for the unsteady aerodynamic coefficients of lift and drag and for the lift-to-drag ratio of several symmetric and cambered airfoils with Gurney flaps. It was found that although the airfoil is considered stationary, starting from a relatively small incidence (about 8 degrees) the flow becomes unsteady due to the unsteadiness of the flow separations occurring at low Reynolds numbers, and the aerodynamic coefficients display periodic oscillations in time. A detailed study is presented in the paper on the influence of various geometric and flow parameters, such as the Gurney flap height, Reynolds number, airfoil relative thickness and relative camber, on the aerodynamic coefficients of lift, drag and lift-to-drag ratio. The flow separation is also studied with the aid of flow visualizations illustrating the changes in the flow pattern at various moments in time.

Summary: In this paper, we present a detailed report on a revised form of simplified and highly stable lattice Boltzmann method (SHSLBM) and its boundary treatment as well as stability analysis. The SHSLBM is a recently developed scheme within lattice Boltzmann framework, which utilizes lattice properties and relationships given by Chapman‐Enskog expansion analysis to reconstruct solutions of macroscopic governing equations recovered from lattice Boltzmann equation and resolved in a predictor‐corrector scheme. Formulations of original SHSLBM are slightly adjusted in the present work to facilitate implementation on body‐fitted mesh. The boundary treatment proposed in this paper offers an analytical approach to interpret no‐slip boundary condition, and the stability analysis in this paper fixes flaws in previous works and reveals a very nice stability characteristic in high Reynolds number scenarios. Several benchmark tests are conducted for comprehensive evaluation of the boundary treatment and numerical validation of stability analysis. It turns out that by adopting the modifications suggested in this work, lower numerical error can be expected. [ABSTRACT FROM AUTHOR]

Resonant three-dimensional nonlinear sloshing in a square-base basin is analysed numerically to investigate swirling instability. The aim of this research is based on understanding how viscosity influences this instability. Four different fluids at increasing Reynolds number were considered in a tank forced to oscillate in a horizontal motion. The present study investigates the tight relation between the energy dissipation and this instability, showing that water tends to dissipate more energy during its rotating motion than the other three liquids characterised by higher viscosity. This aspect is strictly linked to the occurrence of free-surface fragmentation and liquid impacts. The numerical solutions are provided using an enhanced version of the Smoothed Particle Hydrodynamics (SPH) model called δ -LES-SPH model which proved to be suitable for the simulation of violent free-surface flows. [ABSTRACT FROM AUTHOR]

The conventional SPH method has been frustrated with the low accuracy originated from the particle inconsistency. The finite particle method (FPM) is an improved SPH method with a higher-order accuracy. However, the numerical accuracy and stability of FPM depend on the uniformity of particles. Facing the disorder particles, the conventional FPM may suffer from an ill-conditioned corrective matrix and is difficult to conduct longtime simulations. A popular and robust particle regularization scheme is the so-called particle shifting technology (PST), which can effectively enhance the accuracy and stability of particle methods. In the context of FPM, PST is analyzed and discussed, and a modified PST (MPST) is proposed. Modified PST saves great amount of computational cost with respect to the conventional PST and acquires better features of accuracy and stability. Finally, the coupled FPM method by combining MPST and δ-SPH is developed to simulate a series of viscous flows. The numerical results indicate that MPST is effective in improving accuracy, stability, and efficiency of PST, and the coupled FPM is shown to be robust for simulating viscous flows and has a higher accuracy and stability. [ABSTRACT FROM AUTHOR]

A two-stage approach to the selection of the parameters of hydraulic channels of the spray nozzles is proposed. On the first stage, the preliminary assessment of their quality is made according to the nature of the flow of the atomized medium using the inviscid incompressible fluid model. On the second stage, the detailed calculation of the Navier-Stokes equations, the thermal conductivity, and the vorticity of the nonisothermal viscous flow are performed, taking into account the phenomena of phase transitions of the real medium for the nozzle designs and their parameters selected at the first stage. The technique of high-quality, simplified, cost-effective computing costs by assessing the impact of the geometric parameters of the sprayer channels to form fuel jets. The calculation of the velocity field and flow lines and flow field transformation to parametric rectangle with an orthogonal grid calculated by numerical conformal mapping are demonstrated. The influence of the channel configuration on the formation of the jet is analyzed. The distribution of velocities in different zones of the channel is estimated from the point of view of the possibility of controlling the spraying characteristics of the injector. [ABSTRACT FROM AUTHOR]

We present the results of axisymmetric and three-dimensional numerical simulations of the flow around a torus in the low Reynolds number regime [10-2; 3×10³] and aspect-ratio 0<Γ=2a/R≤2 (core diameter over toroidal radius). It is shown that as Γ→0, consistent with intuition and the results from the literature, the flow tends to that of a two-dimensional circular cylinder while for Γ→2 the flow is that around a bluff obstacle. It has been observed that in a small region of the Re - Γ phase space, the flow develops an axisymmetric recirculation detached from the torus and with a vorticity distribution that resembles the Hill vortex. In the range 0<Γ≤2, several different regimes have been observed; the peculiarities of each regime are analyzed and, whenever possible, similarities and differences with other classical flows are discussed. [ABSTRACT FROM AUTHOR]

In this paper, an accurate semi-implicit rotational projection method is introduced to solve the Navier-Stokes equations for incompressible flow simulations. The accuracy of the fractional step procedure is investigated for the standard finite-difference method, and the discrete forms are presented with arbitrary orders or accuracy. In contrast to the previous semi-implicit projection methods, herein, an alternative way is proposed to decouple pressure from the momentum equation by employing the principle form of the pressure Poisson equation. This equation is based on the divergence of the convective terms and incorporates the actual pressure in the simulations. As a result, the accuracy of the method is not affected by the common choice of the pseudo-pressure in the previous methods. Also, the velocity correction step is redefined, and boundary conditions are introduced accordingly. Several numerical tests are conducted to assess the robustness of the method for second and fourth orders of accuracy. The results are compared with the solutions obtained from a typical high-resolution fully explicit method and available benchmark reports. Herein, the numerical tests are consisting of simulations for the Taylor-Green vortex, lid-driven square cavity, and vortex-wall interaction. It is shown that the present method can preserve the order of accuracy for both velocity and pressure fields in second-order and high-order simulations. Furthermore, a very good agreement is observed between the results of the present method and benchmark simulations. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We propose a tailored finite point method (TFPM) for solving a quasilinear time-dependent Burgers' equation with a small coefficient of viscosity. The selected basis functions for the TFPM automatically fit the properties of the local solution in time and space simultaneously. The stability and error analysis for the TFPM are given. We also demonstrate the efficiency of the proposed scheme on relatively coarse meshes. The numerical results indicate that the TFPM achieves high accuracy and effectively captures the shock solutions. [ABSTRACT FROM PUBLISHER]

The moving least square meshfree method is used to solve the Reynolds-averaged Navier-Stokes equations with two different turbulence models: the renormalisation group (RNG) κ-ε model and the Wilcox κ-ε model. The moving least square approach with clouds-of-points reconstruction, which can provide results from highly anisotropic clouds of points, is adopted to approximate the spatial derivatives. Both the subsonic and transonic viscous flows around RAE2822 airfoil are simulated. The pressure coefficients of the airfoil surface are calculated, the Mach number contours of the flow fields are presented, and the mean velocity profiles of the boundary layer at different locations are investigated. Some unsteady viscous flow simulation results are also presented. The simulation results show a good agreement with the experiment results and other numerical simulation results. Overall, the simulation results demonstrate that the proposed meshfree numerical algorithm is accurate and capable of modelling turbulence flows around airfoils. [ABSTRACT FROM AUTHOR]

The main interest of the present investigation is to generate exact solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous electrically conducting fluid flow motion and stability due to disks moving towards each other or in opposite directions with a constant velocity. Making use of the analytic solution, the description of possible conditions of motion is based on the exact solutions of the Navier-Stokes equations. Both stationary and transient cases have been considered. The stability of motion is analyzed for different initial perturbations. Different types of stability were found according to whether the disks moved towards or away from each other.

A numerical methodology is developed to combine the advantages of adaptive mesh refinement (AMR) and interface sharpening technique. A five-equation compressible multiphase model with capillary and viscous effects is considered. The solver employs a wave propagation method along with the Tangent of Hyperbola for INterface Capturing (THINC) scheme. To calculate interface normal and curvature, an implicit filtering method is introduced which transforms the sharpened volume fraction variable to a variant with smoothed distribution. The accuracy and performance of our method is assessed through its application to multiple compressible interface problems ranging from high-Mach number shock–interface interaction to gravity driven flows with viscosity and surface tension effects. The results obtained for one-dimensional shock-tube and tin–air interaction problems are shown to compare well with analytical data. The flow patterns predicted for shock–bubble interaction and under-water explosion match those from the landmark experimental and numerical studies. Furthermore, the trends and values predicted for spike position in the Rayleigh–Taylor instability and bubble’s center location in bubble rising are consistent with those found in literature. Particularly, it is shown that the coupled AMR-THINC method remarkably prevents excessive interface smearing and captures delicate interfacial features such as shear-induced instabilities encountered in shock–bubble interaction. [ABSTRACT FROM AUTHOR]

The unsteady flow field past a two-dimensional permeable square cylinder was predicted by an updated CE/SE method. The periodic patterns of streamline and vortex shedding were obtained. The evolution of lift and drag coefficients were analysed. Results of 2D computations were compared with the experimental data. It found that the Reynolds number dominated the magnitude and frequency of the vorticity given porosity and Darcy number. It proved that the CE/SE method was an effective tool for predicting viscous flows in porous media. [ABSTRACT FROM AUTHOR]

Global linear stability analysis combined with computational fluid dynamics (CFD) is considered useful for understanding the physics of fluid flows. However, the numerical techniques of global linear stability analysis for compressible flows have not been well established in comparison with those for incompressible flows. In this study, we develop and assess a set of appropriate numerical techniques required to conduct a global linear stability analysis for compressible flows. For the eigensystem analysis, the Arnoldi method combined with time integration is in effect to preserve the memory (RAM) size of the computer. The compact difference scheme is used for the CFD analysis from the viewpoints of computing accurate global modes and saving memory by reducing the number of grid points to obtain the necessary spatial resolution. To assess the proposed method, two-dimensional compressible flow problems, including regularized cavity flow, flow around a square cylinder, and the compressible mixing layer, are analyzed, and it is confirmed that the proposed method can obtain accurate mode shapes, growth rate, and frequency of the corresponding global modes. In addition, influences and an appropriate formulation of the outflow boundary conditions are investigated. Results reveal that the outflow boundary causes spurious unstable modes in the global linear stability analysis, and the radiation and outflow boundary condition and the extension of the computational domain with grid stretching keep the spurious unstable modes to a minimum. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A ghost fluid based computational tool is developed to study a wide range of compressible multiphase flows involving strong shocks and contact discontinuities while accounting for surface tension, viscous stresses and gravitational forces. The solver utilizes constrained reinitialization method to predict the interface configuration at each time step. Surface tension effect is handled via an exact interface Riemann problem solver. Interfacial viscous stresses are approximated by considering continuous velocity and viscous stress across the interface. To assess the performance of the solver several benchmark problems are considered: One-dimensional gas-water shock tube problem, shock-bubble interaction, air cavity collapse in water, underwater explosion, Rayleigh-Taylor Instability, and ellipsoidal drop oscillations. Results obtained from the numerical simulations indicate that the numerical methodology performs reasonably well in predicting flow features and exhibit a very good agreement with prior experimental and numerical observations. To further examine the accuracy of the developed ghost fluid solver, the obtained results are compared to those by a conventional diffuse interface solver. The comparison shows the capability of our ghost fluid method in reproducing the experimentally observed flow characteristics while revealing more details regarding topological changes of the interface. [ABSTRACT FROM AUTHOR]

Flow of viscous fluids are not usually discussed in detail in general and basic courses of physics. This is due in part to the fact that the Navier-Stokes equation has analytical solution only for a few restricted cases, while more sophisticated problems can only be solved by numerical methods. In this text, we present a computer simulation of wind tunnel, i.e., we present a set of programs to solve the Navier-Stokes equation for an arbitrary object inserted in a wind tunnel. The tunnel enables us to visualize the formation of vortices behind object, the so-called von Kármán vortices, and calculate the drag force on the object. We believe that this numerical wind tunnel can support the teacher and allow a more elaborate discussion of viscous flow. The potential of the tunnel is exemplified by the study of the drag on a simplified model of wing whose angle of attack can be controlled. A link to download the programs that make up the tunnel appears at the end. [ABSTRACT FROM AUTHOR]

Cell-centered finite volume method with multistage time-stepping is successfully applied to two-dimensional mass-weighted, time-averaged Navier-Stokes equations for the computation of viscous flows. In the cellcentered scheme, flow quantities are associated with the center of a cell. Convective fluxes at the cell faces are evaluated by means of upwind Roe Flux Differencing Scheme (Roe FDS) with Monotone Upwind Schemes for Scalar Conservation Laws (MUSCL) approach. Green’s theorem is employed for evaluation of gradients in computation of viscous fluxes. Five stage hybrid time-stepping scheme is implemented for integration to steady state. Convergence is accelerated by utilizing local time stepping and residual smoothing. The accuracy of the present Navier-Stokes solver is verified by comparing flat-plate laminar boundary-layer solutions with theoretical solutions of Blasius and by comparing laminar airfoil solutions with those available in literature. Convergence down to machine zero attained in the computations indicates a good sign for the efficiency of the present solver. Turbulence closure for Reynolds stresses is obtained using two-layer algebraic eddy viscosity model of Baldwin and Lomax. Computed results for turbulent flows are validated with available experimental results.

The fundamental nature of viscous incompressible flow is investigated by integrating the first and second laws of thermodynamics. The free energy of fluid, the fundamental thermodynamic function for system equilibrium, is shown to be a synthetic combination of the entropy production rate, flow steadiness and Lagrange function (kinetic energy - potential energy). When the flow is stationary and there is no energy exchange at the boundary, the principle of minimum entropy production rate in the thermodynamics of irreversible processes is extended to the space integration of the flow field. The results for minimizing the dynamic drag of fluid flow are discussed. [ABSTRACT FROM AUTHOR]

The fundamental nature of viscous incompressible flow is investigated by integrating the first and second laws of thermodynamics. The free energy of fluid, the fundamental thermodynamic function for system equilibrium, is shown to be a synthetic combination of the entropy production rate, flow steadiness and Lagrange function (kinetic energy - potential energy). When the flow is stationary and there is no energy exchange at the boundary, the principle of minimum entropy production rate in the thermodynamics of irreversible processes is extended to the space integration of the flow field. The results for minimizing the dynamic drag of fluid flow are discussed. [ABSTRACT FROM AUTHOR]