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Volume 34, Issue 2
A Genuinely Two-Dimensional HLL-Type Approximate Riemann Solver for Hypo-Elastic Plastic Flow

Zhiqiang Zeng, Chengliang Feng, Xiaotao Zhang, Shengtao Zhang & Tiegang Liu

DOI: 10.4208/cicp.OA-2022-0314

Commun. Comput. Phys., 34 (2023), pp. 318-356.

Published online: 2023-09

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  • Abstract

In this work, a genuinely two-dimensional HLL-type approximate Riemann solver is proposed for hypo-elastic plastic flow. To consider the effects of wave interaction from both the $x$- and $y$-directions, a corresponding 2D elastic-plastic approximate solver is constructed with elastic-plastic transition embedded. The resultant numerical flux combines one-dimensional numerical flux in the central region of the cell edge and two-dimensional flux in the cell vertex region. The stress is updated separately by using the velocity obtained with the above approximate Riemann solver. Several numerical tests, including genuinely two-dimensional examples, are presented to test the performances of the proposed method. The numerical results demonstrate the credibility of the present 2D approximate Riemann solver.

  • Keywords

Elastic plastic flow, elastic-plastic transition, multi-dimensional effect, two-dimensional approximate Riemann solver.

  • AMS Subject Headings

35L45, 35Q35, 74C05, 74M20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-34-318, author = {Zeng , ZhiqiangFeng , ChengliangZhang , XiaotaoZhang , Shengtao and Liu , Tiegang}, title = {A Genuinely Two-Dimensional HLL-Type Approximate Riemann Solver for Hypo-Elastic Plastic Flow}, journal = {Communications in Computational Physics}, year = {2023}, volume = {34}, number = {2}, pages = {318--356}, abstract = {

In this work, a genuinely two-dimensional HLL-type approximate Riemann solver is proposed for hypo-elastic plastic flow. To consider the effects of wave interaction from both the $x$- and $y$-directions, a corresponding 2D elastic-plastic approximate solver is constructed with elastic-plastic transition embedded. The resultant numerical flux combines one-dimensional numerical flux in the central region of the cell edge and two-dimensional flux in the cell vertex region. The stress is updated separately by using the velocity obtained with the above approximate Riemann solver. Several numerical tests, including genuinely two-dimensional examples, are presented to test the performances of the proposed method. The numerical results demonstrate the credibility of the present 2D approximate Riemann solver.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2022-0314}, url = {http://global-sci.org/intro/article_detail/cicp/21971.html} }
TY - JOUR T1 - A Genuinely Two-Dimensional HLL-Type Approximate Riemann Solver for Hypo-Elastic Plastic Flow AU - Zeng , Zhiqiang AU - Feng , Chengliang AU - Zhang , Xiaotao AU - Zhang , Shengtao AU - Liu , Tiegang JO - Communications in Computational Physics VL - 2 SP - 318 EP - 356 PY - 2023 DA - 2023/09 SN - 34 DO - http://doi.org/10.4208/cicp.OA-2022-0314 UR - https://global-sci.org/intro/article_detail/cicp/21971.html KW - Elastic plastic flow, elastic-plastic transition, multi-dimensional effect, two-dimensional approximate Riemann solver. AB -

In this work, a genuinely two-dimensional HLL-type approximate Riemann solver is proposed for hypo-elastic plastic flow. To consider the effects of wave interaction from both the $x$- and $y$-directions, a corresponding 2D elastic-plastic approximate solver is constructed with elastic-plastic transition embedded. The resultant numerical flux combines one-dimensional numerical flux in the central region of the cell edge and two-dimensional flux in the cell vertex region. The stress is updated separately by using the velocity obtained with the above approximate Riemann solver. Several numerical tests, including genuinely two-dimensional examples, are presented to test the performances of the proposed method. The numerical results demonstrate the credibility of the present 2D approximate Riemann solver.

Zhiqiang Zeng, Chengliang Feng, Xiaotao Zhang, Shengtao Zhang & Tiegang Liu. (2023). A Genuinely Two-Dimensional HLL-Type Approximate Riemann Solver for Hypo-Elastic Plastic Flow. Communications in Computational Physics. 34 (2). 318-356. doi:10.4208/cicp.OA-2022-0314
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