An iterative Riemann solver for systems of hyperbolic conservation law s, with application to hyperelastic solid mechanics
In this paper we present a general iterative method for the solution of the Riemann problem for hyperbolic systems of PDEs. The method is based on the multiple shooting method for free boundary value problems. We demonstrate the method by solving one-dimensional Riemann problems for hyperelastic solid mechanics. Even for conditions representative of routine laboratory conditions and military ballistics, dramatic differences are seen between the exact and approximate Riemann solution. The greatest discrepancy arises from misallocation of energy between compressional and thermal modes by the approximate solver, resulting in nonphysical entropy and temperature estimates. Several pathological conditions arise in common practice, and modifications to the method to handle these are discussed. These include points where genuine nonlinearity is lost, degeneracies, and eigenvector deficiencies that occur upon melting.
- Research Organization:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Sponsoring Organization:
- USDOE Director. Office of Science. Office of Advanced Scientific Computing Research. Mathematical Information and Computational Sciences Division, Department of Energy Laboratory Directed Research and Development award; California Institute of Technology Center, Accelerated Strategic Computing Initiative. Academic Strategic Alliances Program. California Institute of Technology Center for the Simulation of Dynamic Response in Materials. Contract B341492 (US)
- DOE Contract Number:
- AC03-76SF00098
- OSTI ID:
- 829986
- Report Number(s):
- LBNL-53795; JCTPAH; R&D Project: 365953; TRN: US200429%%118
- Journal Information:
- Journal of Computational Physics, Vol. 193, Issue 1; Other Information: Journal Publication Date: 01/01/2004; PBD: 6 Aug 2003; ISSN 0021-9991
- Country of Publication:
- United States
- Language:
- English
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