Volume 9, Issue 3
1D Exact Elastic-Perfectly Plastic Solid Riemann Solver and Its Multi-Material Application

Si Gao & Tiegang Liu

Adv. Appl. Math. Mech., 9 (2017), pp. 621-650.

Published online: 2018-05

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  • Abstract

The equation of state (EOS) plays a crucial role in hyperbolic conservation laws for the compressible fluid. Whereas, the solid constitutive model with elasticplastic phase transition makes the analysis of the solid Riemann problem more diffi- cult. In this paper, one-dimensional elastic-perfectly plastic solid Riemann problem is investigated and its exact Riemann solver is proposed. Different from previous works treating the elastic and plastic phases integrally, we resolve the elastic wave and plastic wave separately to understand the complicate nonlinear waves within the solid and then assemble them together to construct the exact Riemann solver for the elasticperfectly plastic solid. After that, the exact solid Riemann solver is associated with the fluid Riemann solver to decouple the fluid-solid multi-material interaction. Numerical tests, including gas-solid, water-solid high-speed impact problems are simulated by utilizing the modified ghost fluid method (MGFM).

  • Keywords

Riemann problem, elastic-plastic solid, ghost fluid method, multi-material flows.

  • AMS Subject Headings

35L50, 35Q74, 74C05, 74F10, 74M20

  • Copyright

COPYRIGHT: © Global Science Press

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