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.