A study of numerical methods for hyperbolic conservation laws with stiff source terms
type: Item
instance of: scholarly article
title: A study of numerical methods for hyperbolic conservation laws with stiff source terms
zbMATH Open document ID: 0682.76053
DOI: 10.1016/0021-9991(90)90097-K
author: H. C. Yee
author: R. J. Leveque
published in: Journal of Computational Physics
publication date: 1990-01-01T00:00:00Z
review text: The proper modeling of nonequilibrium gas dynamics is required in certain regimes of hypersonic flow. For inviscid flow this gives a system of conservation laws coupled with source terms representing the chemistry. Often a wide range of time scales is present in the problem, leading to numerical difficulties as in stiff systems of ordinary differential equations. Stability can be achieved by using implicit methods, but other numerical difficulties are observed. The behavior of typical numerical methods on a model advection equation with a parameter-dependent source term is studied. Two approaches to incorporate the source terms are utilized: MacCormack type predictor-corrector methods with flux limiters and splitting methods in which the fluid dynamics and chemistry are handled in separate steps. Comparisons over a wide range of parameter values are made. On the whole, the splitting methods perform somewhat better. In the stiff case, a numerical phenomenon of incorrect propagation speeds of discontinuities is observed and explained. Using the model scalar equation, we show that this is due to the introduction of nonequilibrium values through numerical dissipation in the advection step.
Mathematics Subject Classification ID: 76N15
Mathematics Subject Classification ID: 76V05
Mathematics Subject Classification ID: 76K05
Mathematics Subject Classification ID: 35L65
zbMATH DE Number: 4118043
zbMATH Keywords: nonequilibrium gas dynamics
zbMATH Keywords: hypersonic flow
zbMATH Keywords: implicit methods
zbMATH Keywords: MacCormack type predictor-corrector methods
zbMATH Keywords: splitting methods
Wikidata QID: Q115142800
MaRDI profile type: Publication
cites work: Q3996820
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full work available at URL: 0021-9991(90)90097-k
OpenAlex ID: W2094710134
description: scientific article; zbMATH DE number 4118043