Collocated finite-volume method for the incompressible Navier-Stokes problem
type: Item
instance of: scholarly article
title: Collocated finite-volume method for the incompressible Navier-Stokes problem
zbMATH Open document ID: 1473.65146
author: Kirill M. Terekhov
published in: Journal of Numerical Mathematics
publication date: 2021-05-12T00:00:00Z
review text: The author considers a collocated finite volume method to approximate incompressible Navier-Stokes equations. The approach of the finite volume method used here is the integration of the equation over subsets of the physical domain, called control volumes, the use of integration by parts, and then the approximation of the terms which appear after integration. These terms are defined over the interfaces of the control volumes. The velocity components and the pressure are approximated by piecewise-linear continuous and piecewise-constant fields, respectively. The scheme obtained satisfies some important physical properties, e.g., it conserves both the mass and momentum. In addition, the method can be applied to general polyhedral grids. It is stated, but without a ``clear'' rigorous proof, that the method demonstrates higher than the first order of accuracy. Several numerical tests are presented to show the efficiency of the method. In particular, this efficiency is shown numerically for both the cases of high and low Reynolds numbers.
reviewed by: Abdallah Bradji
Mathematics Subject Classification ID: 65M08
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 76M12
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 7347666
zbMATH Keywords: finite volume method
zbMATH Keywords: Navier-Stokes equations
zbMATH Keywords: inf-sup condition
zbMATH Keywords: collocation method
describes a project that uses: BiCGstab
describes a project that uses: Gmsh
describes a project that uses: Netgen
describes a project that uses: INMOST
MaRDI profile type: Publication
full work available at URL: jnma-2020-0008
OpenAlex ID: W3084003684
cites work: A nine-point finite volume scheme for the simulation of diffusion in heterogeneous media
cites work: Computational design for long-term numerical integration of the equations of fluid motion: two-dimensional incompressible flow. Part I
cites work: Stream function-vorticity driven cavity solution using \(p\) finite elements
cites work: A robust ILU with pivoting based on monitoring the growth of the inverse factors
cites work: Solutions of 3D Navier-Stokes benchmark problems with adaptive finite elements
cites work: On conservation laws of Navier-Stokes Galerkin discretizations
cites work: The numerical solution of the Navier-Stokes equations for an incompressible fluid
cites work: Exact fully 3D Navier–Stokes solutions for benchmarking
cites work: Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities
cites work: High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method
cites work: Q3197536
cites work: Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface
cites work: High quality preconditioning of a general symmetric positive definite matrix based on its \(U^T U + U^T R + R^T U\)-decomposition
cites work: Q5576913
cites work: Difference analogues of orthogonal decompositions, basic differential operators and some boundary problems of mathematical physics. I
cites work: Crout Versions of ILU for General Sparse Matrices
cites work: A new pivoting strategy for Gaussian elimination
cites work: An octree-based solver for the incompressible Navier-Stokes equations with enhanced stability and low dissipation
cites work: Conservation properties of unstructured staggered mesh schemes
cites work: Numerical study of the turbulent flow past an airfoil with trailing edge separation
cites work: Q4338821
cites work: NETGEN: An advancing front 2D/3D-mesh generator based on abstract rules
cites work: BiCGstab(\(l\)) and other hybrid Bi-CG methods
cites work: Cell-centered finite-volume method for heterogeneous anisotropic poromechanics problem
cites work: Cell-centered nonlinear finite-volume methods for the heterogeneous anisotropic diffusion problem
cites work: Cell-centered finite-volume method for elastic deformation of heterogeneous media with full-tensor properties
cites work: Finite volume method for coupled subsurface flow problems. I: Darcy problem
DOI: 10.1515/JNMA-2020-0008
description: scientific article; zbMATH DE number 7347666