TY - JOUR
T1 - A Genuinely Two-Dimensional Approximate Riemann Solver with Stress Continuity for Hypo-Elastic Solids
AU - Zeng , Zhiqiang
AU - Cao , Kui
AU - Feng , Chengliang
AU - Wang , Yibo
AU - Liu , Tiegang
JO - Communications in Computational Physics
VL - 4
SP - 1113
EP - 1155
PY - 2024
DA - 2024/10
SN - 36
DO - http://doi.org/10.4208/cicp.OA-2024-0118
UR - https://global-sci.org/intro/article_detail/cicp/23495.html
KW - Hypo-elastic solid, Riemann problem, two-dimensional approximate Riemann solver, stress continuity, path-conservation.
AB - <p style="text-align: justify;">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.</p>