Revisiting the method of characteristics via a convex hull algorithm
arXiv:1409.0291 · doi:10.1016/j.jcp.2015.05.043
Abstract
We revisit the method of characteristics for shock wave solutions to nonlinear hyperbolic problems and we describe a novel numerical algorithm - the convex hull algorithm (CHA) - in order to compute, both, entropy dissipative solutions (satisfying all relevant entropy inequalities) and entropy conservative (or multivalued) solutions to nonlinear hyperbolic conservation laws. Our method also applies to Hamilton-Jacobi equations and other problems endowed with a method of characteristics. From the multivalued solutions determined by the method of characteristic, our algorithm "extracts" the entropy dissipative solutions, even after the formation of shocks. It applies to, both, convex or non-convex flux/Hamiltonians. We demonstrate the relevance of the proposed approach with a variety of numerical tests including a problem from fluid dynamics.
14 pages
Cited by in corpus (4)
- Mesh-free error integration in arbitrary dimensions: a numerical study of discrepancy functions
- The Transport-based Mesh-free Method (TMM) and its applications in finance: a review
- Parametric Interpolation Framework for 1-D Scalar Conservation Laws with Non-Convex Flux Functions
- An algorithm (CoDeFi) for overcoming the curse of dimensionality in mathematical finance