A Genuinely 2D Well-Balanced Method for Elastic-Plastic Flow in Cylindrically Symmetric Coordinates

Abstract

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.