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Volume 36, Issue 4
A Genuinely Two-Dimensional Approximate Riemann Solver with Stress Continuity for Hypo-Elastic Solids

Zhiqiang Zeng, Kui Cao, Chengliang Feng, Yibo Wang & Tiegang Liu

DOI: 10.4208/cicp.OA-2024-0118

Commun. Comput. Phys., 36 (2024), pp. 1113-1155.

Published online: 2024-10

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  • Abstract

The inability to maintain stress continuity across a contact discontinuity is a well-known limitation of some Godunov-type methods developed for gas when directly employed for hypo-elastic solid simulations. Interestingly, this drawback persists in multi-dimensional computations, even when a genuinely multi-dimensional approximate Riemann solver is utilized. To address this challenge, a genuinely two-dimensional Riemann solver is constructed with the enforcement of stress continuity. Subsequently, a path has been constructed by using the present one-dimensional approximate Riemann solver which ensures the stress continuity. Based upon the established path, a discretization method for stress equation is developed by utilizing the path-conservative DLM (Dal Maso, LeFloch, and Murat) approach. Numerical tests demonstrate that the proposed approximate Riemann solver effectively preserves stress continuity, thereby eliminating nonphysical numerical oscillations.

  • Keywords

Hypo-elastic solid, Riemann problem, two-dimensional approximate Riemann solver, stress continuity, path-conservation.

  • AMS Subject Headings

35L45, 35Q35, 74C05, 74M20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-36-1113, author = {Zeng , ZhiqiangCao , KuiFeng , ChengliangWang , Yibo and Liu , Tiegang}, title = {A Genuinely Two-Dimensional Approximate Riemann Solver with Stress Continuity for Hypo-Elastic Solids}, journal = {Communications in Computational Physics}, year = {2024}, volume = {36}, number = {4}, pages = {1113--1155}, abstract = {

The inability to maintain stress continuity across a contact discontinuity is a well-known limitation of some Godunov-type methods developed for gas when directly employed for hypo-elastic solid simulations. Interestingly, this drawback persists in multi-dimensional computations, even when a genuinely multi-dimensional approximate Riemann solver is utilized. To address this challenge, a genuinely two-dimensional Riemann solver is constructed with the enforcement of stress continuity. Subsequently, a path has been constructed by using the present one-dimensional approximate Riemann solver which ensures the stress continuity. Based upon the established path, a discretization method for stress equation is developed by utilizing the path-conservative DLM (Dal Maso, LeFloch, and Murat) approach. Numerical tests demonstrate that the proposed approximate Riemann solver effectively preserves stress continuity, thereby eliminating nonphysical numerical oscillations.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2024-0118}, url = {http://global-sci.org/intro/article_detail/cicp/23495.html} }
TY - JOUR T1 - A Genuinely Two-Dimensional Approximate Riemann Solver with Stress Continuity for Hypo-Elastic Solids AU - Zeng , Zhiqiang AU - Cao , Kui AU - Feng , Chengliang AU - Wang , Yibo AU - Liu , Tiegang JO - Communications in Computational Physics VL - 4 SP - 1113 EP - 1155 PY - 2024 DA - 2024/10 SN - 36 DO - http://doi.org/10.4208/cicp.OA-2024-0118 UR - https://global-sci.org/intro/article_detail/cicp/23495.html KW - Hypo-elastic solid, Riemann problem, two-dimensional approximate Riemann solver, stress continuity, path-conservation. AB -

The inability to maintain stress continuity across a contact discontinuity is a well-known limitation of some Godunov-type methods developed for gas when directly employed for hypo-elastic solid simulations. Interestingly, this drawback persists in multi-dimensional computations, even when a genuinely multi-dimensional approximate Riemann solver is utilized. To address this challenge, a genuinely two-dimensional Riemann solver is constructed with the enforcement of stress continuity. Subsequently, a path has been constructed by using the present one-dimensional approximate Riemann solver which ensures the stress continuity. Based upon the established path, a discretization method for stress equation is developed by utilizing the path-conservative DLM (Dal Maso, LeFloch, and Murat) approach. Numerical tests demonstrate that the proposed approximate Riemann solver effectively preserves stress continuity, thereby eliminating nonphysical numerical oscillations.

Zeng , ZhiqiangCao , KuiFeng , ChengliangWang , Yibo and Liu , Tiegang. (2024). A Genuinely Two-Dimensional Approximate Riemann Solver with Stress Continuity for Hypo-Elastic Solids. Communications in Computational Physics. 36 (4). 1113-1155. doi:10.4208/cicp.OA-2024-0118
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