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Volume 17, Issue 2
A Genuinely 2D Well-Balanced Method for Elastic-Plastic Flow in Cylindrically Symmetric Coordinates

Zhiqiang Zeng, Weixiong Yuan, Chengliang Feng, Tiegang Liu & Shengtao Zhang

Adv. Appl. Math. Mech., 17 (2025), pp. 599-632.

Published online: 2024-12

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  • Abstract

In this work, a genuinely two-dimensional method is proposed for elastic-plastic flow in cylindrically symmetric coordinates. The numerical fluxes are obtained by constructing a genuinely two-dimensional approximate Riemann solver that incorporates consideration of the geometric source term and elastic-plastic transition. The resultant genuine 2D numerical flux combines one-dimensional numerical flux in the central region of the cell edge and two-dimensional flux in the cell vertex region to take wave interaction into account. To deal with the geometry singularity, we establish the equations with removed singularity. For a given stationary state, we prove that the present method is well-balanced. Several numerical tests are presented to verify the performances of the proposed method. The numerical results demonstrate the credibility of the present method.

  • AMS Subject Headings

35L45, 35Q35, 74C05, 74M20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-17-599, author = {Zeng , ZhiqiangYuan , WeixiongFeng , ChengliangLiu , Tiegang and Zhang , Shengtao}, title = {A Genuinely 2D Well-Balanced Method for Elastic-Plastic Flow in Cylindrically Symmetric Coordinates}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2024}, volume = {17}, number = {2}, pages = {599--632}, abstract = {

In this work, a genuinely two-dimensional method is proposed for elastic-plastic flow in cylindrically symmetric coordinates. The numerical fluxes are obtained by constructing a genuinely two-dimensional approximate Riemann solver that incorporates consideration of the geometric source term and elastic-plastic transition. The resultant genuine 2D numerical flux combines one-dimensional numerical flux in the central region of the cell edge and two-dimensional flux in the cell vertex region to take wave interaction into account. To deal with the geometry singularity, we establish the equations with removed singularity. For a given stationary state, we prove that the present method is well-balanced. Several numerical tests are presented to verify the performances of the proposed method. The numerical results demonstrate the credibility of the present method.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2022-0317}, url = {http://global-sci.org/intro/article_detail/aamm/23736.html} }
TY - JOUR T1 - A Genuinely 2D Well-Balanced Method for Elastic-Plastic Flow in Cylindrically Symmetric Coordinates AU - Zeng , Zhiqiang AU - Yuan , Weixiong AU - Feng , Chengliang AU - Liu , Tiegang AU - Zhang , Shengtao JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 599 EP - 632 PY - 2024 DA - 2024/12 SN - 17 DO - http://doi.org/10.4208/aamm.OA-2022-0317 UR - https://global-sci.org/intro/article_detail/aamm/23736.html KW - Elastic-plastic flow, cylindrically symmetric coordinates, well-balanced, twodimensional approximate Riemann solver. AB -

In this work, a genuinely two-dimensional method is proposed for elastic-plastic flow in cylindrically symmetric coordinates. The numerical fluxes are obtained by constructing a genuinely two-dimensional approximate Riemann solver that incorporates consideration of the geometric source term and elastic-plastic transition. The resultant genuine 2D numerical flux combines one-dimensional numerical flux in the central region of the cell edge and two-dimensional flux in the cell vertex region to take wave interaction into account. To deal with the geometry singularity, we establish the equations with removed singularity. For a given stationary state, we prove that the present method is well-balanced. Several numerical tests are presented to verify the performances of the proposed method. The numerical results demonstrate the credibility of the present method.

Zeng , ZhiqiangYuan , WeixiongFeng , ChengliangLiu , Tiegang and Zhang , Shengtao. (2024). A Genuinely 2D Well-Balanced Method for Elastic-Plastic Flow in Cylindrically Symmetric Coordinates. Advances in Applied Mathematics and Mechanics. 17 (2). 599-632. doi:10.4208/aamm.OA-2022-0317
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