One-sided difference approximations for nonlinear conservation laws
1981 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 36, 321-351 p.Article in journal (Refereed) Published
We analyze one-sided or upwind finite difference approximations to hyperbolic partial differential equations and, in particular, nonlinear conservation laws. Second order schemes are designed for which we prove both nonlinear stability and that the entropy condition is satisfied for limit solutions. We show that no such stable approximation of order higher than two is possible. These one-sided schemes have desirable properties for shock calculations. We show that the proper switch used to change the direction in the upwind differencing across a shock is of great importance. New and simple schemes are developed for which we prove qualitative properties such as sharp monotone shock profiles, existence, uniqueness, and stability of discrete shocks. Numerical examples are given.
Place, publisher, year, edition, pages
1981. Vol. 36, 321-351 p.
Computer and Information Science
IdentifiersURN: urn:nbn:se:kth:diva-90514OAI: oai:DiVA.org:kth-90514DiVA: diva2:505755
NR 201408052012-02-242012-02-24Bibliographically approved