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Stretched Cartesian grids for solution of the incompressible Navier-Stokes equations

Stretched Cartesian grids for solution of the incompressible Navier-Stokes equations
Stretched Cartesian grids for solution of the incompressible Navier-Stokes equations
Two Cartesian grid stretching functions are investigated for solving the unsteady incompressible Navier-Stokes equations using the pressure-velocity formulation. The first function is developed for the Fourier method and is a generalization of earlier work. This function concentrates more points at the centre of the computational box while allowing the box to remain finite. The second stretching function is for the second-order central finite difference scheme, which uses a staggered grid in the computational domain. This function is derived to allow a direct discretization of the Laplacian operator in the pressure equation while preserving the consistent behaviour exhibited by the uniform grid scheme. Both functions are analysed for their effects on the matrix of the discretized pressure equation. It is shown that while the second function does not spoil the matrix diagonal dominance, the first one can. Limits to stretching of the first method are derived for the cases of mappings in one and two directions. A limit is also derived for the second function in order to prevent a strong distortion of a sine wave. The performances of the two types of stretching are examined in simulations of periodic co-flowing jets and a time developing boundary layer.
incompressible Navier-Stokes equations, Poisson equation, stretching function
0271-2091
897-918
Avital, E.J.
37c1edd0-b9c3-4751-be1e-c61505671ae8
Sandham, N.D.
d7f8726e-a0d8-4298-adb5-c82246d376f5
Luo, K.H.
1c9be6c6-e956-4b12-af13-32ea855c69f3
Avital, E.J.
37c1edd0-b9c3-4751-be1e-c61505671ae8
Sandham, N.D.
d7f8726e-a0d8-4298-adb5-c82246d376f5
Luo, K.H.
1c9be6c6-e956-4b12-af13-32ea855c69f3

Avital, E.J., Sandham, N.D. and Luo, K.H. (2000) Stretched Cartesian grids for solution of the incompressible Navier-Stokes equations. International Journal for Numerical Methods in Fluids, 33 (6), 897-918. (doi:10.1002/1097-0363(20000730)33:6<897::AID-FLD37>3.0.CO;2-4).

Record type: Article

Abstract

Two Cartesian grid stretching functions are investigated for solving the unsteady incompressible Navier-Stokes equations using the pressure-velocity formulation. The first function is developed for the Fourier method and is a generalization of earlier work. This function concentrates more points at the centre of the computational box while allowing the box to remain finite. The second stretching function is for the second-order central finite difference scheme, which uses a staggered grid in the computational domain. This function is derived to allow a direct discretization of the Laplacian operator in the pressure equation while preserving the consistent behaviour exhibited by the uniform grid scheme. Both functions are analysed for their effects on the matrix of the discretized pressure equation. It is shown that while the second function does not spoil the matrix diagonal dominance, the first one can. Limits to stretching of the first method are derived for the cases of mappings in one and two directions. A limit is also derived for the second function in order to prevent a strong distortion of a sine wave. The performances of the two types of stretching are examined in simulations of periodic co-flowing jets and a time developing boundary layer.

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More information

Published date: 2000
Keywords: incompressible Navier-Stokes equations, Poisson equation, stretching function

Identifiers

Local EPrints ID: 21332
URI: https://eprints.soton.ac.uk/id/eprint/21332
ISSN: 0271-2091
PURE UUID: 61c7e1a0-6a9c-4938-9575-66fc57823e56

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Date deposited: 14 Mar 2006
Last modified: 17 Jul 2017 16:26

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Contributors

Author: E.J. Avital
Author: N.D. Sandham
Author: K.H. Luo

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