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Volume 15, Issue 2
A Compact Eulerian Interface–Capturing Algorithm for Compressible Multimaterial Elastic–Plastic Flows with Mie–Grüneisen Equation of State

Xiang Li, Dong-Jun Ma, Nan-Sheng Liu & Pei Wang

Adv. Appl. Math. Mech., 15 (2023), pp. 485-521.

Published online: 2022-12

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  • Abstract

This paper presents an Eulerian diffuse-interface method using a high-order compact difference scheme for simulating elastic-plastic flows with the Mie–Grüneisen (MG) equation of state (EoS). For simulations of multimaterial problems, numerical errors were generated in the material discontinuities owing to inconsistent treatment of the convective terms. Based on the normal-stress-based mechanical equilibrium assumption for elastic-plastic solids, we introduce an improved form of the consistent localized artificial diffusivity (LAD) method to ensure an oscillation-free interface for velocity and normal stress. The proposed algorithm uses a hyperelastic model. A mixture type of the model system was formed by combining the conservation equations for the basic conserved variables, an equation of a unified deviatoric tensor describing solid deformation, and an additional set of equations for solving the material quantities in the MG EoS. Several one- and two-dimensional problems with various discontinuities, including the elastic-plastic Richtmyer–Meshkov instability, were considered for testing the proposed method.

  • AMS Subject Headings

74F10, 76T99, 74S20

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COPYRIGHT: © Global Science Press

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@Article{AAMM-15-485, author = {Li , XiangMa , Dong-JunLiu , Nan-Sheng and Wang , Pei}, title = {A Compact Eulerian Interface–Capturing Algorithm for Compressible Multimaterial Elastic–Plastic Flows with Mie–Grüneisen Equation of State}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2022}, volume = {15}, number = {2}, pages = {485--521}, abstract = {

This paper presents an Eulerian diffuse-interface method using a high-order compact difference scheme for simulating elastic-plastic flows with the Mie–Grüneisen (MG) equation of state (EoS). For simulations of multimaterial problems, numerical errors were generated in the material discontinuities owing to inconsistent treatment of the convective terms. Based on the normal-stress-based mechanical equilibrium assumption for elastic-plastic solids, we introduce an improved form of the consistent localized artificial diffusivity (LAD) method to ensure an oscillation-free interface for velocity and normal stress. The proposed algorithm uses a hyperelastic model. A mixture type of the model system was formed by combining the conservation equations for the basic conserved variables, an equation of a unified deviatoric tensor describing solid deformation, and an additional set of equations for solving the material quantities in the MG EoS. Several one- and two-dimensional problems with various discontinuities, including the elastic-plastic Richtmyer–Meshkov instability, were considered for testing the proposed method.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2021-0019}, url = {http://global-sci.org/intro/article_detail/aamm/21278.html} }
TY - JOUR T1 - A Compact Eulerian Interface–Capturing Algorithm for Compressible Multimaterial Elastic–Plastic Flows with Mie–Grüneisen Equation of State AU - Li , Xiang AU - Ma , Dong-Jun AU - Liu , Nan-Sheng AU - Wang , Pei JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 485 EP - 521 PY - 2022 DA - 2022/12 SN - 15 DO - http://doi.org/10.4208/aamm.OA-2021-0019 UR - https://global-sci.org/intro/article_detail/aamm/21278.html KW - Multimaterial elastic-plastic flow, Eulerian solid-dynamics, high-order accurate schemes, compact finite difference, localized artificial diffusivity. AB -

This paper presents an Eulerian diffuse-interface method using a high-order compact difference scheme for simulating elastic-plastic flows with the Mie–Grüneisen (MG) equation of state (EoS). For simulations of multimaterial problems, numerical errors were generated in the material discontinuities owing to inconsistent treatment of the convective terms. Based on the normal-stress-based mechanical equilibrium assumption for elastic-plastic solids, we introduce an improved form of the consistent localized artificial diffusivity (LAD) method to ensure an oscillation-free interface for velocity and normal stress. The proposed algorithm uses a hyperelastic model. A mixture type of the model system was formed by combining the conservation equations for the basic conserved variables, an equation of a unified deviatoric tensor describing solid deformation, and an additional set of equations for solving the material quantities in the MG EoS. Several one- and two-dimensional problems with various discontinuities, including the elastic-plastic Richtmyer–Meshkov instability, were considered for testing the proposed method.

Xiang Li, Dong-Jun Ma, Nan-Sheng Liu & Pei Wang. (2022). A Compact Eulerian Interface–Capturing Algorithm for Compressible Multimaterial Elastic–Plastic Flows with Mie–Grüneisen Equation of State. Advances in Applied Mathematics and Mechanics. 15 (2). 485-521. doi:10.4208/aamm.OA-2021-0019
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