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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 elastic-plastic phase transition makes the analysis of the solid Riemann problem more difficult. 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 elastic-perfectly 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).

  • AMS Subject Headings

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

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-9-621, author = {Gao , Si and Liu , Tiegang}, title = {1D Exact Elastic-Perfectly Plastic Solid Riemann Solver and Its Multi-Material Application}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {9}, number = {3}, pages = {621--650}, abstract = {

The equation of state (EOS) plays a crucial role in hyperbolic conservation laws for the compressible fluid. Whereas, the solid constitutive model with elastic-plastic phase transition makes the analysis of the solid Riemann problem more difficult. 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 elastic-perfectly 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).

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2015.m1340}, url = {http://global-sci.org/intro/article_detail/aamm/12167.html} }
TY - JOUR T1 - 1D Exact Elastic-Perfectly Plastic Solid Riemann Solver and Its Multi-Material Application AU - Gao , Si AU - Liu , Tiegang JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 621 EP - 650 PY - 2018 DA - 2018/05 SN - 9 DO - http://doi.org/10.4208/aamm.2015.m1340 UR - https://global-sci.org/intro/article_detail/aamm/12167.html KW - Riemann problem, elastic-plastic solid, ghost fluid method, multi-material flows. AB -

The equation of state (EOS) plays a crucial role in hyperbolic conservation laws for the compressible fluid. Whereas, the solid constitutive model with elastic-plastic phase transition makes the analysis of the solid Riemann problem more difficult. 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 elastic-perfectly 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).

Si Gao & Tiegang Liu. (2020). 1D Exact Elastic-Perfectly Plastic Solid Riemann Solver and Its Multi-Material Application. Advances in Applied Mathematics and Mechanics. 9 (3). 621-650. doi:10.4208/aamm.2015.m1340
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