Flux Difference Splitting for Three-Dimensional Steady Incompressible Navier-Stokes Equations in Curvilinear Co-Ordinates

Oosterlee, Cornelis W.; Ritzdorf, Hubert

doi:10.1002/(sici)1097-0363(19960830)23:4<347::aid-fld424>3.0.co;2-o

Cited by 12 publications

(1 citation statement)

References 29 publications

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“…The present work extends the collocated finite-volume method considered earlier in References [23][24][25] to handle moving meshes. It realizes a general concept of stable flux discretization of saddle-point systems for vectors of several unknowns 3 using a combination of harmonic averaging point concept 26 and a flux-difference splitting method [27][28][29][30] for one-sided fluxes with positive matrix coefficients. 31,32 Single-sided fluxes are required to be linearity preserving, 33 that is, exact on linear solutions.…”

Section: Introductionmentioning

confidence: 99%

Dynamic adaptive moving mesh finite‐volume method for the blood flow and coagulation modeling

Terekhov

Butakov

Danilov

et al. 2023

Numer Methods Biomed Eng

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In this work, we develop numerical methods for the solution of blood flow and coagulation on dynamic adaptive moving meshes. We consider the blood flow as a flow of incompressible Newtonian fluid governed by the Navier–Stokes equations. The blood coagulation is introduced through the additional Darcy term, with a permeability coefficient dependent on reactions. To this end, we introduce moving mesh collocated finite‐volume methods for the Navier–Stokes equations, advection–diffusion equations, and a method for the stiff cascade of reactions. A monolithic nonlinear system is solved to advance the solution in time. The finite volume method for the Navier–Stokes equations features collocated arrangement of pressure and velocity unknowns and a coupled momentum and mass flux. The method is conservative and inf‐sup stable despite the saddle point nature of the system. It is verified on a series of analytical problems and applied to the blood flow problem in the deforming domain of the right ventricle, reconstructed from a time series of computed tomography scans. At last, we demonstrate the ability to model the coagulation process in deforming microfluidic capillaries.

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Section: Introductionmentioning

confidence: 99%

Dynamic adaptive moving mesh finite‐volume method for the blood flow and coagulation modeling

Terekhov

Butakov

Danilov

et al. 2023

Numer Methods Biomed Eng

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Comparison of Implicit Multigrid Schemes for Three-Dimensional Incompressible Flows

2002

Journal of Computational Physics

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To develop a robust and efficient computational flow simulation tool for incompressible flow applications, a number of different implicit multigrid schemes for solving the three-dimensional incompressible Navier-Stokes equations are compared in the current study. These schemes consist of a common full approximation storage (FAS) multigrid algorithm implemented in conjunction with three different implicit schemes, which include a modified point Gauss relaxation, a standard Gauss-Seidel line relaxation, and the Beam-Warming alternating direction implicit (ADI) scheme. The flow solver used in the study is based on artificial compressibility and uses a third-order upwind difference for the convective terms and a second-order central difference for the viscous terms. The efficiency of each implicit multigrid scheme is assessed in terms of the computing time required for two laminar flow problems: the entry flow through a 90• bent square duct, and the steady-state and unsteady flows past a prolate spheroid at incidence with an axis ratio of 4 : 1. It is found that implementation of Neumann boundary conditions on the coarse grid in terms of the flow variable correction rather than the flow variable itself is essential for obtaining good convergence in the collocated finite difference discretization. The results of steady-state flow computations show that all the implicit multigrid schemes yield more than 50% computational time savings over their single grid counterparts, and the point or line relaxation multigrid scheme outperforms the ADI multigrid scheme by at least a factor of 2. However, in unsteady flow computations, the computational time saving of the multigrid scheme is less than that in steady-state cases. The current study concludes that the FAS multigrid algorithm implemented with the modified point Gauss relaxation scheme is preferable for simulating both steady-state and time-dependent incompressible flows. c 2002 Elsevier Science (USA)

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CFD Analysis of Tube Type Heat Exchanger of a Split Air Conditioner

Sinha

Sikarwar

2021

Lecture Notes in Mechanical Engineering

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Flux Difference Splitting for Three-Dimensional Steady Incompressible Navier-Stokes Equations in Curvilinear Co-Ordinates

Cited by 12 publications

References 29 publications

Dynamic adaptive moving mesh finite‐volume method for the blood flow and coagulation modeling

Dynamic adaptive moving mesh finite‐volume method for the blood flow and coagulation modeling

Comparison of Implicit Multigrid Schemes for Three-Dimensional Incompressible Flows

CFD Analysis of Tube Type Heat Exchanger of a Split Air Conditioner

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