A Genuinely Two-Dimensional HLL-Type Approximate Riemann Solver for Hypo-Elastic Plastic Flow

Abstract

In this work, a genuinely two-dimensional HLL-type approximate Riemann solver is proposed for hypo-elastic plastic flow. To consider the effects of wave interaction from both the $x$- and $y$-directions, a corresponding 2D elastic-plastic approximate solver is constructed with elastic-plastic transition embedded. The resultant numerical flux combines one-dimensional numerical flux in the central region of the cell edge and two-dimensional flux in the cell vertex region. The stress is updated separately by using the velocity obtained with the above approximate Riemann solver. Several numerical tests, including genuinely two-dimensional examples, are presented to test the performances of the proposed method. The numerical results demonstrate the credibility of the present 2D approximate Riemann solver.