A Compact Eulerian Interface–Capturing Algorithm for Compressible Multimaterial Elastic–Plastic Flows with Mie–Grüneisen Equation of State

A Compact Eulerian Interface–Capturing Algorithm for Compressible Multimaterial Elastic–Plastic Flows with Mie–Grüneisen Equation of State

Year:    2023

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

Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 2 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2021-0019

Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 2 : pp. 485–521

Published online:    2023-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    37

Keywords:    Multimaterial elastic-plastic flow Eulerian solid-dynamics high-order accurate schemes compact finite difference localized artificial diffusivity.

Author Details

Xiang Li

Dong-Jun Ma

Nan-Sheng Liu

Pei Wang