Year: 2017
Communications in Computational Physics, Vol. 22 (2017), Iss. 5 : pp. 1224–1257
Abstract
For 2D elastic-plastic flows with the hypo-elastic constitutive model and von Mises' yielding condition, the non-conservative character of the hypo-elastic constitutive model and the von Mises' yielding condition make the construction of the solution to the Riemann problem a challenging task. In this paper, we first analyze the wave structure of the Riemann problem and develop accordingly a Four-Rarefaction wave approximate Riemann Solver with Elastic waves (FRRSE). In the construction of FRRSE one needs to use an iterative method. A direct iteration procedure for four variables is complex and computationally expensive. In order to simplify the solution procedure we develop an iteration based on two nested iterations upon two variables, and our iteration method is simple in implementation and efficient. Based on FRRSE as a building block, we propose a 2nd-order cell-centered Lagrangian numerical scheme. Numerical results with smooth solutions show that the scheme is of second-order accuracy. Moreover, a number of numerical experiments with shock and rarefaction waves demonstrate the scheme is essentially non-oscillatory and appears to be convergent. For shock waves the present scheme has comparable accuracy to that of the scheme developed by Maire et al., while it is more accurate in resolving rarefaction waves.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2016-0173
Communications in Computational Physics, Vol. 22 (2017), Iss. 5 : pp. 1224–1257
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 34
-
An efficient second-order cell-centered Lagrangian discontinuous Galerkin method for two-dimensional elastic-plastic flows
Niu, Panyu | Qing, Fang | Wang, Cheng | Jia, Zupeng | Wang, WanliPhysics of Fluids, Vol. 36 (2024), Iss. 3
https://doi.org/10.1063/5.0200567 [Citations: 1] -
A cell-centered implicit-explicit Lagrangian scheme for a unified model of nonlinear continuum mechanics on unstructured meshes
Boscheri, Walter | Chiocchetti, Simone | Peshkov, IlyaJournal of Computational Physics, Vol. 451 (2022), Iss. P.110852
https://doi.org/10.1016/j.jcp.2021.110852 [Citations: 10] -
A higher-order Lagrangian discontinuous Galerkin hydrodynamic method for solid dynamics
Lieberman, Evan J. | Liu, Xiaodong | Morgan, Nathaniel R. | Luscher, Darby J. | Burton, Donald E.Computer Methods in Applied Mechanics and Engineering, Vol. 353 (2019), Iss. P.467
https://doi.org/10.1016/j.cma.2019.05.006 [Citations: 19] -
A friction interface model for multi-material interactions in a Eulerian framework
Wang, Wanli | Wang, Cheng | Yang, Tonghui | Chen, DongpingJournal of Computational Physics, Vol. 433 (2021), Iss. P.110057
https://doi.org/10.1016/j.jcp.2020.110057 [Citations: 16] -
A 3D cell-centered ADER MOOD Finite Volume method for solving updated Lagrangian hyperelasticity on unstructured grids
Boscheri, Walter | Loubère, Raphaël | Maire, Pierre-HenriJournal of Computational Physics, Vol. 449 (2022), Iss. P.110779
https://doi.org/10.1016/j.jcp.2021.110779 [Citations: 9] -
Thirty Years of the Finite Volume Method for Solid Mechanics
Cardiff, P. | Demirdžić, I.Archives of Computational Methods in Engineering, Vol. 28 (2021), Iss. 5 P.3721
https://doi.org/10.1007/s11831-020-09523-0 [Citations: 51] -
The complete exact Riemann solution for one-dimensional elastic–perfectly plastic Riemann problem
Li, Xiao | Zhai, Jiayin | Shen, ZhijunComputer Methods in Applied Mechanics and Engineering, Vol. 390 (2022), Iss. P.114346
https://doi.org/10.1016/j.cma.2021.114346 [Citations: 2] -
HLLEPJ and HLLCEPJ Riemann solvers for the Wilkins model of elastoplasticity
Serezhkin, A.
Journal of Computational Physics, Vol. 492 (2023), Iss. P.112419
https://doi.org/10.1016/j.jcp.2023.112419 [Citations: 3] -
A second-order cell-centered Lagrangian scheme with a HLLC Riemann solver of elastic and plastic waves for two-dimensional elastic-plastic flows
Cheng, Jun-Bo | Liu, Li | Jiang, Song | Yu, Ming | Liu, ZhanliJournal of Computational Physics, Vol. 413 (2020), Iss. P.109452
https://doi.org/10.1016/j.jcp.2020.109452 [Citations: 9] -
Harten-Lax-van Leer-discontinuities with elastic waves (HLLD-e) approximate Riemann solver for two-dimensional elastic-plastic flows with slip/no-slip interface boundary conditions
Zhao, Fuyu | Wang, Cheng | Jia, Xiyu | Wang, WanliComputers & Fluids, Vol. 265 (2023), Iss. P.106015
https://doi.org/10.1016/j.compfluid.2023.106015 [Citations: 2] -
An HLLC-type approximate Riemann solver for two-dimensional elastic-perfectly plastic model
Li, Xiao | Zhai, Jiayin | Shen, ZhijunJournal of Computational Physics, Vol. 448 (2022), Iss. P.110675
https://doi.org/10.1016/j.jcp.2021.110675 [Citations: 3] -
The Discontinuous Galerkin Material Point Method for variational hyperelastic–plastic solids
Renaud, Adrien | Heuzé, Thomas | Stainier, LaurentComputer Methods in Applied Mechanics and Engineering, Vol. 365 (2020), Iss. P.112987
https://doi.org/10.1016/j.cma.2020.112987 [Citations: 8]