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Commun. Comput. Phys., 36 (2024), pp. 1113-1155.
Published online: 2024-10
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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.
}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2024-0118}, url = {http://global-sci.org/intro/article_detail/cicp/23495.html} }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.