Title: Colocated pressure-velocity coupling in finite difference methods

Authors: Mikael Ersson

Addresses: Materials Science and Engineering, KTH Royal Institute of Technology, Brinellvägen 23, 100 44 Stockholm, Sweden

Abstract: A simple method to be used for colocated pressure-velocity coupling in incompressible flows is presented with a full derivation. A number of standard test cases are shown that demonstrate the ability of the method to produce accurate results. The method avoids spurious pressure oscillations while keeping the pressure Poisson equation stencil compact. This is obtained by discretising the continuity and pressure derivatives with first order differences with opposite directions, i.e., backward difference for continuity and forward difference for pressure (BCFP). The equations are also approximated using a forward difference for continuity and a backward difference for pressure (FCBP). In order to obtain a second order approximation the mean between BCFP and FCBP is used, i.e., a central difference. The paper gives a useful alternative to existing methods for pressure-velocity coupling in finite difference methods in which a staggered arrangement is not desirable.

Keywords: finite difference method; FDM; spurious oscillations; colocated variable arrangement; collocated variable arrangement.

DOI: 10.1504/PCFD.2019.102037

Progress in Computational Fluid Dynamics, An International Journal, 2019 Vol.19 No.5, pp.273 - 281

Accepted: 05 Dec 2017
Published online: 05 Aug 2019 *

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