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

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

Year:    2025

Author:    Zhiqiang Zeng, Weixiong Yuan, Chengliang Feng, Tiegang Liu, Shengtao Zhang

Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 2 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2022-0317

Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 2 : pp. 599–632

Published online:    2025-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    34

Keywords:    Elastic-plastic flow cylindrically symmetric coordinates well-balanced twodimensional approximate Riemann solver.

Author Details

Zhiqiang Zeng

Weixiong Yuan

Chengliang Feng

Tiegang Liu

Shengtao Zhang