Analyse and Suppression Method of Wall Heating Error for Elastic-Plastic Problem

doi:10.19596/j.cnki.1001-246x.8869

Abstract

Abstract:

This paper studies numerical scheme and suppression method of wall heating error for elastic-plastic flow with cell-centered Lagrange Godunov method. Provide the viscosity correction equation of Godunov scheme, describe the procedure of a viscous shock formation and propagation with a jump type initial data, and analyze the relationship between the viscosity behavior of the correction equation and wall heating error. On this basis, a new HLLC-type approximate Riemann solver is proposed. In this solver, an adaptive heat conduction viscosity is introduced to suppress wall heating error of internal energy and density at the interface; What's more, an additional contact velocity is proposed to suppress the over-heating phenomenon of deviatoric stress.

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

CLC Number:

Xiao LI, Zhijun SHEN, Hongping GUO, Jun FANG, Hongping ZHANG. Analyse and Suppression Method of Wall Heating Error for Elastic-Plastic Problem[J]. Chinese Journal of Computational Physics, 2024, 41(5): 569-581.

Figures/Tables 11

Fig.1 Mesh division

Fig.2 Wave structure of HLLCE solver

Fig.3 Wave structure of HLLE solver

Fig.4 Numerical results of HLLCE and HLLE for Exp.1 with an infinite yield strength (a) internal energy; (b) deviatoric stress

Fig.5 Numerical results of HLLCE and HLLE for Exp.1 with Y0=3×108 Pa (a) internal energy; (b) deviatoric stress

Fig.6 Numerical results of HLLCE and HLLE for Exp.2 (a) internal energy; (b)deviatoric stress

Fig.7 Numerical results of HLLCE, HLLE and HLLCEN for Exp.3 (a) internal energy; (b) deviatoric stress

Fig.8 Numerical results of HLLCE, HLLE and HLLCEN for Exp.4 (a) internal energy; (b) deviatoric stress

Fig.9 Numerical results of HLLCE, HLLE and HLLCEN for Exp.5 (a) internal energy; (b) deviatoric stress

Fig.10 Variations of Taylor rod length and energy with time for 2D Taylor problem (a) length; (b) energy

Fig.11 Density contour of Taylor rod

References 16

1	SAMBASIVAN S K , SHASHKOV M J , BURTON D E . A cell-centered lagrangian finite volume approach for computing elasto-plastic response of solids in cylindrical axisymmetric geometries[J]. Journal of Computational Physics, 2013, 237, 251- 288. DOI
2	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, 626- 665. DOI
3	LI Xiao , ZHAI Jiayin , SHEN Zhijun . An HLLC-type approximate Riemann solver for two-dimensional elastic-perfectly plastic model[J]. Journal of Computational Physics, 2022, 448, 110675. DOI
4	WILKINS M L. Calculation of elastic-plastic flow: UCRL-7322[R]. Livermore: Lawrence Livermore Laboratory, 1963.
5	TRANGENSTEIN J A , COLELLA P . A higher-order Godunov method for modeling finite deformation in elastic-plastic solids[J]. Communications on Pure and Applied Mathematics, 1991, 44 (1): 41- 100. DOI
6	GAVRILYUK S L , FAVRIE N , SAUREL R . Modelling wave dynamics of compressible elastic materials[J]. Journal of Computational Physics, 2008, 227 (5): 2941- 2969. DOI
7	MENSHOV I S , MISCHENKO A V , SEREJKIN A A . Numerical modeling of elastoplastic flows by the Godunov method on moving Eulerian grids[J]. Mathematical Models and Computer Simulations, 2014, 6, 127- 141. DOI
8	沈智军, 谢亚伟, 闫伟. 一种减少壁热误差的自适应热粘性[J]. 计算物理, 2012, 29 (6): 807- 814. DOI
9	李肖, 孙晨, 沈智军. 一维理想弹塑性流体的数值模拟及壁热现象的抑制[J]. 计算物理, 2020, 37 (5): 539- 550. DOI
10	NOH W F . Errors for calculations of strong shocks using an artificial viscosity and an artificial heat flux[J]. Journal of Computational Physics, 1987, 72 (1): 78- 120. DOI
11	GEHMEYR M , CHENG B , MIHALAS D . Noh's constant-velocity shock problem revisited[J]. Shock Waves, 1997, 7, 255- 274. DOI
12	SHEN Zhijun , YAN Wei , LV Guixia . Behavior of viscous solutions in Lagrangian formulation[J]. Journal of Computational Physics, 2010, 229 (12): 4522- 4543. DOI
13	CHENG Junbo , LIU Li , JIANG Song , et al. A second-order cell-centered Lagrangian scheme with a HLLC Riemann solver of elastic and plastic waves for two-dimensional elastic-plastic flows[J]. Journal of Computational Physics, 2020, 413, 109452. DOI
14	SEREZHKIN A . HLLEPJ and HLLCEPJ riemann solvers for the wilkins model of elastoplasticity[J]. Journal of Computational Physics, 2023, 492, 112419. DOI
15	周海兵, 熊俊, 刘文韬, 等. 拉氏数值模拟中的人工粘性方法[J]. 计算物理, 2010, 27 (6): 829- 832. DOI
16	MENIKOFF R . Errors when shock waves interact due to numerical shock width[J]. SIAM Journal on Scientific Computing, 1994, 15 (5): 1227- 1242. DOI

[1]	Xinyue XI, Xiaocheng GUO, Chi WANG. An HLLC Riemann Solver for MHD Tangential Discontinuities [J]. Chinese Journal of Computational Physics, 2022, 39(3): 286-296.
[2]	Liji WANG, Hongping GUO, Zhijun SHEN. Reducing Entropy Production in a Lagrangian Method [J]. Chinese Journal of Computational Physics, 2022, 39(2): 179-190.
[3]	Chuang XUE, Xingdong LI, Wenjun SUN, Wenhua YE, Xianjue PENG. A Multi-material Five-equation-reduced Model and Artificial Compression Method for Interface Capture [J]. Chinese Journal of Computational Physics, 2021, 38(3): 257-268.
[4]	SUN Chen, LI Xiao, SHEN Zhijun. A Godunov Method with Staggered Lagrangian Discretization Applicable to Isentropic Flows [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2020, 37(5): 529-538.
[5]	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.
[6]	LIU Yan, MAO Dekang. An ADRS Approximated Riemann Solver in Compatible Lagrangian Method [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2020, 37(2): 140-152.
[7]	JI Meixuan, YU Xijun, SONG Mingyang. ALE Discontinuous Finite Element Method for One-dimensional Fluid Dynamics Equations with Chemical Reactions [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2020, 37(1): 1-9.
[8]	WU Zongduo, YAN Jin, ZONG Zhi, ZHAO Yong. A Multi-component Mie-Grüneisen Mixture Model Based on HLLC Algorithm [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2020, 37(1): 55-62.
[9]	REN Jian, SHEN Zhijun, YAN Wei, YUAN Guangwei. A Robust Riemann Solver Without Artificial Intervention [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2018, 35(1): 1-12.
[10]	LIU Jingjing, ZENG Xianyang, NI Guoxi. Euler Numerical Methods for Reactive Flow with General Equation of States in Two Dimensions [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2018, 35(1): 29-38.
[11]	SHANGGUAN Zining, ZHOU Xiuli, SONG Xin, CHEN Qian. Numerical Simulation of Typical Free Surface Flow with SPH-ALE [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2017, 34(6): 641-650.
[12]	SHEN Zhijun, XIE Yawei, YAN Wei. Wall Heating and Adaptive Heat Conduction Viscosity [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2012, 29(6): 807-814.
[13]	LEI Guodong, LI Wanai, Ren Yuxin. A High-order Unstructured-grid WENO FVM for Compressible Flow Computation [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2011, 28(5): 633-640.
[14]	LEI Guodong, REN Yuxin. A Second-order Hybrid Rotated Riemann Solver for Multi-dimensional Euler Equations on Unstructured Meshes [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2009, 26(6): 799-805.
[15]	ZHANG Deliang, WANG Jingtao, WANG Gang. High-order CE/SE Method and Applications [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2009, 26(2): 211-220.