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Volume 12, Issue 1
A Robust Riemann Solver for Multiple Hydro-Elastoplastic Solid Mediums

Ruo Li, Yanli Wang & Chengbao Yao

Adv. Appl. Math. Mech., 12 (2020), pp. 212-250.

Published online: 2019-12

[An open-access article; the PDF is free to any online user.]

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  • Abstract

We propose a robust approximate solver for the hydro-elastoplastic solid material, a general constitutive law extensively applied in explosion and high speed impact dynamics, and provide a natural transformation between the fluid and solid in the case of phase transitions. The hydrostatic components of the solid is described by a family of general Mie-Grüneisen equation of state (EOS), while the deviatoric component includes the elastic phase, linearly hardened plastic phase and fluid phase. The approximate solver provides the interface stress and normal velocity by an iterative method. The well-posedness and convergence of our solver are proved with mild assumptions on the equations of state. The proposed solver is applied in computing the numerical flux at the phase interface for our compressible multi-medium flow simulation on Eulerian girds. Several numerical examples, including Riemann problems, shock-bubble interactions, implosions and high speed impact applications, are presented to validate the approximate solver.

  • AMS Subject Headings

76L05, 74H15, 76T30, 68U20, 47E05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

rli@math.pku.edu.cn (Ruo Li)

wangyanliwyl@gmail.com (Yanli Wang)

yaocheng@pku.edu.cn (Chengbao Yao)

  • BibTex
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  • TXT
@Article{AAMM-12-212, author = {Li , RuoWang , Yanli and Yao , Chengbao}, title = {A Robust Riemann Solver for Multiple Hydro-Elastoplastic Solid Mediums}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2019}, volume = {12}, number = {1}, pages = {212--250}, abstract = {

We propose a robust approximate solver for the hydro-elastoplastic solid material, a general constitutive law extensively applied in explosion and high speed impact dynamics, and provide a natural transformation between the fluid and solid in the case of phase transitions. The hydrostatic components of the solid is described by a family of general Mie-Grüneisen equation of state (EOS), while the deviatoric component includes the elastic phase, linearly hardened plastic phase and fluid phase. The approximate solver provides the interface stress and normal velocity by an iterative method. The well-posedness and convergence of our solver are proved with mild assumptions on the equations of state. The proposed solver is applied in computing the numerical flux at the phase interface for our compressible multi-medium flow simulation on Eulerian girds. Several numerical examples, including Riemann problems, shock-bubble interactions, implosions and high speed impact applications, are presented to validate the approximate solver.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2019-0039}, url = {http://global-sci.org/intro/article_detail/aamm/13425.html} }
TY - JOUR T1 - A Robust Riemann Solver for Multiple Hydro-Elastoplastic Solid Mediums AU - Li , Ruo AU - Wang , Yanli AU - Yao , Chengbao JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 212 EP - 250 PY - 2019 DA - 2019/12 SN - 12 DO - http://doi.org/10.4208/aamm.OA-2019-0039 UR - https://global-sci.org/intro/article_detail/aamm/13425.html KW - Riemann solver, Mie-Grüneisen, hydro-elastoplastic solid, multi-medium flow. AB -

We propose a robust approximate solver for the hydro-elastoplastic solid material, a general constitutive law extensively applied in explosion and high speed impact dynamics, and provide a natural transformation between the fluid and solid in the case of phase transitions. The hydrostatic components of the solid is described by a family of general Mie-Grüneisen equation of state (EOS), while the deviatoric component includes the elastic phase, linearly hardened plastic phase and fluid phase. The approximate solver provides the interface stress and normal velocity by an iterative method. The well-posedness and convergence of our solver are proved with mild assumptions on the equations of state. The proposed solver is applied in computing the numerical flux at the phase interface for our compressible multi-medium flow simulation on Eulerian girds. Several numerical examples, including Riemann problems, shock-bubble interactions, implosions and high speed impact applications, are presented to validate the approximate solver.

Ruo Li, Yanli Wang & Chengbao Yao. (2019). A Robust Riemann Solver for Multiple Hydro-Elastoplastic Solid Mediums. Advances in Applied Mathematics and Mechanics. 12 (1). 212-250. doi:10.4208/aamm.OA-2019-0039
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