Revisiting the method of characteristics via a convex hull algorithm

We revisit the method of characteristics for shock wave solutions to nonlinear hyperbolic problems and we propose a novel numerical algorithm—the convex hull algorithm (CHA)—which allows us to compute both entropy dissipative solutions (satisfying all entropy inequalities) and entropy conservative (...

Full description

Saved in:
Bibliographic Details
Published in:Journal of computational physics 2015-10, Vol.298, p.95-112
Main Authors: LeFloch, Philippe G., Mercier, Jean-Marc
Format: Article
Language:English
Subjects:
Algorithms
Compressible fluid
Computational geometry
Convexity
Dissipation
Entropy
Hulls (structures)
Hyperbolic equations
Mathematical models
Mathematics
Method of characteristics
Numerical algorithm
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We revisit the method of characteristics for shock wave solutions to nonlinear hyperbolic problems and we propose a novel numerical algorithm—the convex hull algorithm (CHA)—which allows us to compute both entropy dissipative solutions (satisfying all entropy inequalities) and entropy conservative (or multi-valued) solutions. From the multi-valued solutions determined by the method of characteristics, our algorithm “extracts” the entropy dissipative solutions, even after the formation of shocks. It applies to both convex and non-convex flux/Hamiltonians. We demonstrate the relevance of the proposed method with a variety of numerical tests, including conservation laws in one or two spatial dimensions and problem arising in fluid dynamics.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2015.05.043