Parallel computation of large amplitude shocks for a system of conservation laws with small

• Type: Chapter or Part of a Book
• Date: 2009

Authors

Hime, G (Author) Other; Vítor Matos (Author) FEP

Book

Title: Proceedings of Symposia in Applied Mathematics

Pages: 643-652

ISBN: ISB: 978-0-8218-4730-5

Indexing

ISI Web of Knowledge - 0 Citations

Other information

Authenticus ID: P-00K-JD2

Abstract (EN): In a recent paper, stable solutions were proved to arise from small amplitude data for an example of conservation laws with a parabolic term possessing the identity as viscosity matrix. The initial data analyzed therein lies outside the elliptic region, and the viscous solutions are related to a bifurcation of planar vector fields with nilpotent singularities studied by Dumortier, Roussarie and Sotomaior (DRS). For non-identity viscosity matrices, the DRS bifurcation is located at the border of the Majda-Pego instability region. The stability proof does not easily generalize for other viscosity matrices: in this work, this issue is studied using numerical simulation. We use a custom high performance parallel Newton solver for the non linear system arising from the Crank-Nicolson finite difference discretization. We present numerical evidence that the stable shocks do not arise from arbitrary small Riemann data with non-identity viscous matrices. However, some of the stable shocks arise from small data if one initial state lies in the elliptic region. In some of these cases, the solution seems to be unaffected by small perturbations.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 10