Exact and approximate solutions of Riemann problems in non-linear elasticity

P.T. Barton, D. Drikakis, E. Romenski, V.A. Titarev

Research output: Contribution to journalArticle

46 Citations (Scopus)

Abstract

Eulerian shock-capturing schemes have advantages for modelling problems involving complex non-linear wave structures and large deformations in solid media. Various numerical methods now exist for solving hyperbolic conservation laws that have yet to be applied to non-linear elastic theory. In this paper one such class of solver is examined based upon characteristic tracing in conjunction with high-order monotonicity preserving weighted essentially non-oscillatory (MPWENO) reconstruction. Furthermore, a new iterative method for finding exact solutions of the Riemann problem in non-linear elasticity is presented. Access to exact solutions enables an assessment of the performance of the numerical techniques with focus on the resolution of the seven wave structure. The governing model represents a special case of a more general theory describing additional physics such as material plasticity. The numerical scheme therefore provides a firm basis for extension to simulate more complex physical phenomena. Comparison of exact and numerical solutions of one-dimensional initial values problems involving three-dimensional deformations is presented.
Original languageEnglish
Pages (from-to)7046-7068
Number of pages23
JournalJournal of Computational Physics
Volume228
Issue number18
DOIs
Publication statusPublished - 1 Oct 2009

Keywords

  • Riemann problem
  • non-linear elasticity
  • solid mechanics
  • WENO

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