Capturing nonclassical shocks in nonlinear elastodynamic with a conservative finite volume scheme - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Interfaces and Free Boundaries Year : 2016

Capturing nonclassical shocks in nonlinear elastodynamic with a conservative finite volume scheme

Nina Aguillon

Abstract

For a model of nonlinear elastodynamics, we construct a finite volume scheme which is able to capture nonclassical shocks (also called undercompressive shocks). Those shocks verify an entropy inequality but are not admissible in the sense of Liu. They verify a kinetic relation which describes the jump, and keeps an information on the equilibrium between a vanishing dispersion and a vanishing diffusion. The scheme pre-sented here is by construction exact when the initial data is an isolated nonclassical shock. In general, it does not introduce any diffusion near shocks, and hence nonclas-sical solutions are correctly approximated. The method is fully conservative and does not use any shock-tracking mesh. This approach is tested and validated on several test cases. In particular, as the nonclassical shocks are not diffused at all, it is possible to obtain large time asymptotics.
Fichier principal
Vignette du fichier
ReconstructionElastoV2.pdf (494.31 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-01116582 , version 1 (13-02-2015)

Licence

Attribution

Identifiers

Cite

Nina Aguillon. Capturing nonclassical shocks in nonlinear elastodynamic with a conservative finite volume scheme. Interfaces and Free Boundaries, 2016, 18 (2), pp.137-159. ⟨10.4171/IFB/360⟩. ⟨hal-01116582⟩
93 View
126 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More