Computation of viscous or nonviscous conservation law by domain decomposition based on asymptotic analysis
Article first published online: 20 JUN 2005
Copyright © 1992 Wiley Periodicals, Inc.
Numerical Methods for Partial Differential Equations
Volume 8, Issue 2, pages 127–142, March 1992
How to Cite
Bourgeat, A. and Garbey, M. (1992), Computation of viscous or nonviscous conservation law by domain decomposition based on asymptotic analysis. Numer. Methods Partial Differential Eq., 8: 127–142. doi: 10.1002/num.1690080204
- Issue published online: 20 JUN 2005
- Article first published online: 20 JUN 2005
- Manuscript Revised: 14 DEC 1990
- Manuscript Received: 29 DEC 1989
An accurate and efficient numerical method has been developed for a nonlinear diffusion convection-dominated problem. The scheme combines asymptotic methods with usual solution techniques for hyperbolic problems. After having localized shock or corner layers and rescaling, first terms of the inner expansion are computed. Using the same concepts gives a method to compute a very accurate solution of the nonlinear conservation law. Because our numerical scheme is based on a uniform approximation throughout the domain, the shock is localized very accurately and there is practically no smearing out. Numerical computations are presented. Another novel feature is the ability to break down the problem according to subdomains of different local behavior, based on asymptotic analysis, which may make it feasible to do computations with different processors.