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A Genuinely Two-Dimensional Approximate Riemann Solver with Stress Continuity for Hypo-Elastic Solids

A Genuinely Two-Dimensional Approximate Riemann Solver with Stress Continuity for Hypo-Elastic Solids

Year:    2024

Author:    Zhiqiang Zeng, Kui Cao, Chengliang Feng, Yibo Wang, Tiegang Liu

Communications in Computational Physics, Vol. 36 (2024), Iss. 4 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2024-0118

Communications in Computational Physics, Vol. 36 (2024), Iss. 4 : pp. 1113–1155

Published online:    2024-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    43

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

Author Details

Zhiqiang Zeng

Kui Cao

Chengliang Feng

Yibo Wang

Tiegang Liu