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During the flow of non-Newtonian fluids in porous media, the relationships between macroscopic quantities are governed by extremely complex microscopic fluid dynamics resulting from solid-fluid interactions. Consequently, the Darcy-scale viscosity exhibited by a shear-thinning fluid depends on the injection velocity, contrarily to the case of Newtonian fluids. In the present work, pore network modelling is used to investigate the relationships between local and macroscopic viscosities during the flow of shear-thinning fluids in 3D porous media. Special efforts are devoted to 1) identifying the influence of the viscosity exhibited by the fluid within the constrictions of the preferential flow paths on the value of Darcy-scale viscosity and 2) proposing an analytical expression to upscale viscosity from the local viscosity values. To go further, the reduction in average hydraulic tortuosity stemming from the directional nature of shear-thinning behavior in 3D porous media will also be quantified. The results of the present study show that Darcy-scale viscosity can be accurately calculated as the flow-rate weighted average of local viscosities in the investigated media. Moreover, the velocity maps provided by the proposed pore network flow simulations are suitable to assess hydraulic tortuosity reduction as compared to the flow of a Newtonian fluid. [ABSTRACT FROM AUTHOR]

In this work, the decoupled finite particle coupled with smoothed particle hydrodynamics (DFP-SPH) method is firstly developed to simulate the viscoelastic fluid flow with free surface. A particle shifting technology is introduced to eliminate the tensile instability and nonuniformity of fluid particles. The motivations and embodiments include: (a) the partial derivatives of physical quantities of velocity, density and viscoelastic stress are calculated based on multivariate Taylor series and dominated contributions from diagonal matrices, which avoid the inversion of encountered ill-conditioned matrices potentially and improve the precision of numerical approximation to a certain extent; (b) a particle shifting technology is added to remove the tensile instability and nonuniformity of fluid particles in the frame of proposed DFP-SPH, and the determination of free surface particles is also proceeded in nature; (c) the dynamic boundary particles possessing computational simplicity are introduced and adopted in the proposed method. A moderate uniformization is proposed to eliminate the spatial effect of nonphysical boundary layers. Subsequently, the accuracy, consistency and convergence of present method are investigated on some benchmarks of Newtonian and Oldroyd-B fluids with analytical solutions. The validity of particle shifting technology in DFP-SPH is verified and multiple inter miscible viscoelastic drops impacting on the rigid wall are simulated and analyzed numerically for the capacity of proposed method. The procedure of jet bulking is well demonstrated through using Newtonian and Oldroyd-B models at different Weissenberg numbers, which possesses flexible free surfaces and tangled interfaces of multifluid layers. Numerical results show that the coupled particle model has a good performance on the viscoelastic fluid flow with free surface. [ABSTRACT FROM AUTHOR]

Non-Newtonian fluids are present in most manufacturing industry processes. Computational models used to describe the rheological behavior of such materials can be costly due to the non-linear behavior of the viscosity. This work presents a parametrized projection-based model reduction approach to address time-dependent generalized Newtonian fluids in a computational framework. We develop our discrete formulation using three ingredients: an offline-online setting for the model reduction based on a proper orthogonal and Tucker decompositions, the finite element method for the discretization of the spatial domain and finite differences for the temporal integration, and the variational multiscale approach as a stabilization technique for both the full and reduced order models. We also evaluate the reduced method with some numerical tests, where the first part involves testing the accuracy of the model reduction method for time as a single parameter of the dynamic reduced problem. The second part involves the solution of parametrized time-dependent reduced problems with the Reynolds number and the power-law index of the fluid as the varying parameters. [ABSTRACT FROM AUTHOR]

In this work, we have developed an updated Lagrangian particle hydrodynamics (ULPH) for Newtonian fluid. Unlike the smoothed particle hydrodynamics, the non-local particle hydrodynamics formulation proposed here is consistent and convergence. Unlike the state-based peridynamics, the discrete particle dynamics proposed here has no internal material bond between particles, and it is not formulated with respect to initial or a fixed referential configuration. In specific, we have shown that (1) the non-local update Lagrangian particle hydrodynamics formulation converges to the conventional local fluid mechanics formulation; (2) the non-local updated Lagrangian particle hydrodynamics can capture arbitrary flow discontinuities without any changes in the formulation, and (3) the proposed non-local particle hydrodynamics is computationally efficient and robust. [ABSTRACT FROM AUTHOR]

We present a model for generalized Newtonian fluid flow through a porous medium. In the model the dependence of the fluid viscosity on the velocity is replaced by a dependence on a smoothed (locally averaged) velocity. With appropriate assumptions on the smoothed velocity, existence of a solution to the model is shown. Two examples of smoothing operators are presented in the appendices. A numerical approximation scheme is presented and an a priori error estimate derived. A numerical example is given illustrating the approximation scheme and the a priori error estimate. [ABSTRACT FROM AUTHOR]

In this paper, three different fractional step methods are designed for the three-field viscoelastic flow problem, whose variables are velocity, pressure and elastic stress. The starting point of our methods is the same as for classical pressure segregation algorithms used in the Newtonian incompressible Navier–Stokes problem. These methods can be understood as an inexact LU block factorization of the original system matrix of the fully discrete problem and are designed at the pure algebraic level. The final schemes allow one to solve the problem in a fully decoupled form, where each equation (for velocity, pressure and elastic stress) is solved separately. The first order scheme is obtained from a straightforward segregation of pressure and elastic stress in the momentum equation, whereas the key point for the second order scheme is a first order extrapolation of these variables. The third order fractional step method relies on Yosida's scheme. Referring to the spatial discretization, either the Galerkin method or a stabilized finite element formulation can be used. We describe the fractional step methods first assuming the former, and then we explain the modifications introduced by the stabilized formulation we employ and that has been proposed in a previous work. This discretization in space shows very good stability, permitting in particular the use of equal interpolation for all variables. [ABSTRACT FROM AUTHOR]

Fluid–structure coupling is addressed through a unified equation for compressible Newtonian fluid flow and elastic solid deformation. This is done by introducing thermodynamics within Cauchy׳s equation through the isothermal compressibility coefficient that is experimentally measurable for both fluids and solids. The vectorial resolution of the governing equation, where every component of velocity vectors and displacement variation vectors is calculated simultaneously in the overall multi-phase system, is characteristic of a monolithic resolution involving no iterative coupling. For system equation closure, mass density and pressure are both re-actualized from velocity vector divergence, when the shear stress tensor within the solid phase is re-actualized from the displacement variation vectors. This novel approach is first validated on a two-phase system, involving a plane fluid–solid interface, through the two following test cases: (i) steady-state compression and (ii) longitudinal and transverse elastic wave propagations. Then the 3D study of compressive fluid injection towards an elastic solid is analyzed from initial time to steady-state evolution. [ABSTRACT FROM AUTHOR]

In this work, we consider the limited fitness for practical use of the Lattice Boltzmann Method for non-Newtonian fluid flows. Several authors have shown that the LBM is capable of correctly simulating those fluids. However, due to stability reasons the modeled viscosity range has to be truncated. The resulting viscosity boundaries are chosen arbitrarily, because the correct simulation Mach number for the physical problem is unknown a priori . This easily leads to corrupt simulation results. A viscosity adaption method (VAM) is derived which drastically improves the applicability of LBM for non-Newtonian fluid flows by adaption of the modeled viscosity range to the actual physical problem. This is done through tuning of the global Mach number to the solution-dependent shear rate. We demonstrate that the VAM can be used to accelerate LBM simulations and improve their accuracy, for both steady state and transient cases. [ABSTRACT FROM AUTHOR]

Abstract: A novel finite element method for the 3d simulation of (many) particles in a Newtonian carrier liquid is presented. The methods features the celebrated one domain approach, a subspace projection method to account for the rigid body motion within the particles and operator splitting. Combined with local mesh refinement the method results in a fast and accurate, though conceptually simple to implement algorithm. Validation is achieved using the sedimentation of one particle and comparing the resulting drag coefficient with theoretical and experimental results. Furthermore, a viscometer is considered, where the effective viscosity of a particle laden fluid is compared with analytic results. [Copyright &y& Elsevier]

• Stabilised finite element method for incompressible non-Newtonian fluid flow. • Full consistency for low-order pairs by using only first-order derivatives. • Linearisation and decoupling of velocity-pressure-viscosity system via extrapolation. • Adaptive timestepping via predictor-corrector approach or fractional step θ -scheme. • Fast physics-based preconditioned Krylov subspace solver. Various materials and solid-fluid mixtures of engineering and biomedical interest can be modelled as generalised Newtonian fluids, as their apparent viscosity depends locally on the flow field. Despite the particular features of such models, it is common practice to combine them with numerical techniques originally conceived for Newtonian fluids, which can bring several issues such as spurious pressure boundary layers, unsuitable natural boundary conditions and coupling terms spoiling the efficiency of nonlinear solvers and preconditioners. In this work, we present a finite element framework dealing with such issues while maintaining low computational cost and simple implementation. The building blocks of our algorithm are (i) an equal-order stabilisation method preserving consistency even for lowest-order discretisations, (ii) robust extrapolation of velocities in the time-dependent case to decouple the rheological law from the overall system, (iii) adaptive time step selection and (iv) a fast physics-based preconditioned Krylov subspace solver, to tackle the relevant range of discretisation parameters including highly varying viscosity. Selected numerical experiments are provided demonstrating the potential of our approach in terms of robustness, accuracy and efficiency for problems of practical interest. [ABSTRACT FROM AUTHOR]

• Development of a refined two-scale model which numerically resolves fluid flow within a fracture in a poroelastic medium. • Complex fluid behaviour can be handled, as demonstrated for a Carreau fluid. • Pressure waves can be captured through inclusion of fluid inertia. • Study of the effect of mesh refinement on propagation velocity and possible pressure oscillations. A refined model is presented which numerically resolves the fluid flow within a fracture inside a saturated poroelastic material. At the discontinuity, the mass balance of the fluid is solved using the velocity profile inside the fracture, with the velocity profile being determined numerically from the momentum balance in the integration points at the discontinuity. The resolution of the mass balance and the velocity profile in the integration points at the discontinuity is coupled to surrounding poroelastic material model in a two-scale approach. The resulting monolithic scheme allows for complex fluid behaviour to be included, which is demonstrated via the inclusion of the fluid inertia and the use of a Carreau fluid. The governing equations are discretised using T-splines, while the fracture is represented by spline-based interface elements, and an implicit time discretisation scheme is used. Mesh refinement studies are carried out for a typical case, which contains a pressurised and propagating fracture. A coarse macro-scale mesh is sufficient to obtain the correct propagation velocities, but a finer mesh is needed to prevent pressure oscillations. Time step refinement studies show the capabilities of the model to capture pressure waves within the fracture. Finally, it is shown that if inertial effects are limited and a Newtonian fluid is used, a fracture scale discretisation using a single element is sufficient. However, for a Carreau fluid or when the problem is inertia-dominated, smaller elements are needed to correctly represent the velocity profile. [ABSTRACT FROM AUTHOR]

[Display omitted] • Cerebrospinal fluid flow is driven by the arterial pulsation. • Net flow velocity in numerical simulations agrees with that in animal experiments. • The net flow velocity is theoretically given by the lubrication theory in analogy with Taylor's swimming sheet model. • Lubrication theory rationalizes the net flow veolocity. The lubrication theory used is analogous to Taylor's swimming sheet model. Cerebrospinal fluid (CSF) flow in the perivascular space (PVS), which surrounds the arteries in the brain, is of paramount importance in the removal of metabolic waste. Despite a number of experimental and numerical studies regarding CSF flow, the underlying mechanics of CSF flow are still debated, especially regarding whether an arterial pulsation can indeed produce net CSF flow velocity. Furthermore, the relationship between CSF flow and arterial wall pulsation has not been fully defined. To clarify these questions, we numerically investigated the CSF flow in the PVS in an axisymmetric channel with a pulsating boundary, where CSF is modeled as an incompressible, Newtonian viscous fluid in non-porous space. Our numerical results show that the net CSF flow velocity driven by the arterial pulsation is consistent with that of previous animal experiments. However, the peak oscillatory velocity is two orders of magnitude larger than the net velocity. Interestingly, the net CSF flow velocity collapses on the analytical solution derived from the lubrication theory in analogy with Taylor's swimming sheet model. [ABSTRACT FROM AUTHOR]

• Mathematical framework and well-conditioned computational tools for resolvent analysis. • A feedback interconnection of the frequency response operator with its adjoint. • Application to channel flows of Newtonian and viscoelastic fluids. Modal and nonmodal analyses of fluid flows provide fundamental insight into the early stages of transition to turbulence. Eigenvalues of the dynamical generator govern temporal growth or decay of individual modes, while singular values of the frequency response operator quantify the amplification of disturbances for linearly stable flows. In this paper, we develop well-conditioned ultraspherical and spectral integration methods for frequency response analysis of channel flows of Newtonian and viscoelastic fluids. Even if a discretization method is well-conditioned, we demonstrate that calculations can be erroneous if singular values are computed as the eigenvalues of a cascade connection of the frequency response operator and its adjoint. To address this issue, we utilize a feedback interconnection of the frequency response operator with its adjoint to avoid computation of inverses and facilitate robust singular value decomposition. Specifically, in contrast to conventional spectral collocation methods, the proposed method (i) produces reliable results in channel flows of viscoelastic fluids at high Weissenberg numbers (∼500); and (ii) does not require a staggered grid for the equations in primitive variables. [ABSTRACT FROM AUTHOR]

A general state-based peridynamics model is developed to simulate transport of fluids in an arbitrary heterogeneous porous medium. The generality encompasses modeling of multiphase, multi-component flow of non-Newtonian and compressible fluids, which is often encountered in but not limited to subsurface reservoirs. Peridynamic model is especially useful for solving non-local problems, such as crack propagation, since it does not assume spatial continuity of field variables. Thus, the formulation presented here, combined with peridynamics-based damage model, can be used to simulate hydraulic fracturing with complex fluids. To demonstrate its capability to simulate multi-phase flow in porous media, the derived model is verified against the analytical Buckley-Leverett solution for immiscible Newtonian two-phase flow. Further, the non-Newtonian two-phase fluid flow in porous media is verified by simulating the polymer flood process involving immiscible displacement of a Newtonian fluid by a non-Newtonian fluid against a generalized solution obtained by Wu et al. [22]. The non-local solutions are shown to be consistent with the corresponding local solutions in limiting cases. Moreover, mass conservation of all the phases is satisfied, irrespective of discretization and extent of non-locality. • Generalized peridynamic model is verified against the analytical solutions. • In the limiting cases, the non-local solution converges to the local solution. • The application of the model to subsurface flow is demonstrated. [ABSTRACT FROM AUTHOR]