TY - JOUR
T1 - A Genuinely 2D Well-Balanced Method for Elastic-Plastic Flow in Cylindrically Symmetric Coordinates
AU - Zeng , Zhiqiang
AU - Yuan , Weixiong
AU - Feng , Chengliang
AU - Liu , Tiegang
AU - Zhang , Shengtao
JO - Advances in Applied Mathematics and Mechanics
VL - 2
SP - 599
EP - 632
PY - 2024
DA - 2024/12
SN - 17
DO - http://doi.org/10.4208/aamm.OA-2022-0317
UR - https://global-sci.org/intro/article_detail/aamm/23736.html
KW - Elastic-plastic flow, cylindrically symmetric coordinates, well-balanced, twodimensional approximate Riemann solver.
AB - <p style="text-align: justify;">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.</p>