Finite difference schemes for incompressible flows in the velocity-impulse density formulation
type: Item
instance of: scholarly article
title: Finite difference schemes for incompressible flows in the velocity-impulse density formulation
zbMATH Open document ID: 0870.76048
author: Jian-Guo Liu
author: Weinan E
published in: Journal of Computational Physics
publication date: 1997-09-22T00:00:00Z
review text: We consider finite difference schemes based on the impulse density variable. We show that the original velocity-impulse density formulation of Oseledets is marginally ill-posed for the inviscid flow, and this has the consequence that some ordinarily stable numerical methods in other formulations become unstable in the velocity-impulse density formulation. We present numerical evidence of this instability. We then discuss the construction of stable finite difference schemes by requiring that at the numerical level the nonlinear terms are convertible to similar terms in the primitive variable formulation.
Mathematics Subject Classification ID: 76M20
Mathematics Subject Classification ID: 76D05
zbMATH DE Number: 987990
zbMATH Keywords: stable schemes
zbMATH Keywords: simplified formulation
zbMATH Keywords: driven cavity flow
zbMATH Keywords: instability
MaRDI profile type: Publication
full work available at URL: jcph.1996.5537
OpenAlex ID: W1983987753
DOI: 10.1006/JCPH.1996.5537
description: scientific article; zbMATH DE number 987990