Numerical Schemes for Hyperbolic Conservation Laws with Stiff Relaxation Terms

✍ Scribed by Shi Jin; C.David Levermore

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 445 KB
• Volume: 126
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1996.0149

✦ Synopsis

was studied by Hsiao and Liu [22] who showed that its solutions exhibit a long-time behavior governed by Hyperbolic systems often have relaxation terms that give them a partially conservative form and that lead to a long-time behavior governed by reduced systems that are parabolic in nature. In this

article it is shown by asymptotic analysis and numerical examples that semidiscrete high resolution methods for hyperbolic conservation laws fail to capture this asymptotic behavior unless the small The first equation above is sometimes referred to as the relaxation rate is resolved by a fine spatial grid. We introduce a porous media equation, in which context the second plays modification of higher order Godunov methods that possesses the the role of Darcy's law.

correct asymptotic behavior, allowing the use of coarse grids (large A somewhat more general system with relaxation that cell Peclet numbers). The idea is to build into the numerical scheme we will use to illustrate the subsequent theory is the asymptotic balances that lead to this behavior. Numerical experiments on 2 ϫ 2 systems verify our analysis.