Numerical Simulation of One-dimensional Elastic-Perfectly Plastic Flow and Suppression of Wall Heating Phenomenon

doi:10.19596/j.cnki.1001-246x.8141

Abstract

Abstract: An HLLC-type approximate Riemann solver is proposed to simulate one-dimensional elastic-perfectly plastic flow with Wilkins model. This Riemann solver introduces plastic wave and has the same wave number with actual physics. The wave speed is determined by characteristic analysis of wave system. The algorithm is simple to implement and does not need iteration. In order to reduce wall heating error in the simulation for strong shock (or rarefaction), wall heating viscosity is designed to effectively suppress the non-physical wall heating phenomenon.

Key words: elastic-plastic flow, plastic wave, Riemann solver, HLLC, wall heating phenomenon

CLC Number:

O354

LI Xiao, SUN Chen, SHEN Zhijun. Numerical Simulation of One-dimensional Elastic-Perfectly Plastic Flow and Suppression of Wall Heating Phenomenon[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2020, 37(5): 539-550.

References

[1] WILKINS M L. Calculation of elastic-plastic flow[J]. Journal of Biological Chemistry, 1964, 280(13):12833-12839.
[2] TRANGENSTEIN J A, COLELLA P. A higher-order Godunov method for modeling finite deformation in elastic-plastic solids[J]. Communications on Pure & Applied Mathematics, 2010, 44(1):41-100.
[3] MILLER G H, COLELLA P. A high-order Eulerian Godunov method for elastic-plastic flow in solids[J]. Journal of Computational Physics, 2001, 167(1):131-176.
[4] BURTON D E, CARNEY T C, MORGAN N R, et al. A cell-centered Lagrangian Godunov-like method for solid dynamics[J]. Computers & Fluids, 2013, 83:33-47.
[5] KLUTH G, DESPRES B. Discretization of hyperelasticity on unstructured mesh with a cell-centered Lagrangian scheme[J]. Journal of Computational Physics, 2010, 229(24):9092-9118.
[6] MAIRE P H, ABGRALL R, BREIL J, et al. A nominally second-order cell-centered Lagrangian scheme for simulating elastic-plastic flows on two-dimensional unstructured grids[J]. Journal of Computational Physics, 2013, 235(Complete):626-665.
[7] GAO S, LIU T G. 1D exact elastic-perfectly plastic solid Riemann solver and its multi-material application[J]. Advances in Applied Mathematics and Mechanics, 2017, 9(03):621-650.
[8] CHENG J B, TORO E F, JIANG S, et al. A high-order cellcentered Lagrangian scheme for one-dimensional elastic-plastic problems[J]. Computers & Fluids, 2015, 122:136-152.
[9] CHENG J B. Harten-Lax-van Leer-contact (HLLC) approximation Riemann solver with elastic waves for one-dimensional elastic-plastic problems[J]. Applied Mathematics and Mechanics, 2016, 37(11):1517-1538.
[10] LIU L, CHENG J B. A multi-material HLLC Riemann solver with both elastic and plastic waves for 1D elastic-plastic flows[J]. Computers and Fluids, 2019, 192:104265.
[11] WANG R L, LIN Z, WEN L, et al. Wall heating and Q&H method in arbitrary n-polygon Lagrange grids finite volume method[J]. Chinese Journal of Computational Physics, 2007, 24(4):407-412.
[12] SHEN Z J, XIE Y W, YAN W. Wall heating and adaptive heat conduction viscosity[J]. Chinese Journal of Computational Physics, 2012, 29(6):807-814.
[13] SHEN Z J, LV G X, SHEN L J. Riemann solver and artificial viscosity in SPH[J]. Mathematica Numerica Sinica, 2006, 28(4):433-448.
[14] VONNEUMANN J, RICHTMYER R D. A method for the numerical calculation of hydrodynamic shocks[J]. Journal of Applied Physics, 1950, 21(3):232-237.

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