Year: 2020
Author: Malte Braack, Utku Kaya
Journal of Computational Mathematics, Vol. 38 (2020), Iss. 1 : pp. 125–141
Abstract
Pressure correction methods constitute the most widely used solvers for the time-dependent Navier-Stokes equations. There are several different pressure correction methods, where each time step usually consists in a predictor step for a non-divergence-free velocity, followed by a Poisson problem for the pressure (or pressure update), and a final velocity correction to obtain a divergence-free vector field. In some situations, the equations for the velocities are solved explicitly, so that the most numerically expensive step is the elliptic pressure problem. We here propose to solve this Poisson problem by a domain decomposition method which does not need any communication between the sub-regions. Hence, this system is perfectly adapted for parallel computation. We show under certain assumptions that this new scheme has the same order of convergence as the original pressure correction scheme (with global projection). Numerical examples for the Stokes system show the effectivity of this new pressure correction method. The convergence order $\mathcal O(k^{ 2})$ for resulting velocity fields can be observed in the norm $l^2(0,T ;L^2(\Omega))$.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1906-m2018-0210
Journal of Computational Mathematics, Vol. 38 (2020), Iss. 1 : pp. 125–141
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Stokes system Navier-Stokes Pressure correction Finite elements.