A second-order cell-centered Lagrangian scheme with a HLLC Riemann solver of elastic and plastic waves for two-dimensional elastic-plastic flows

Abstract

In this paper, we propose a fast and efficient second-order cell-centered Lagrangian scheme for 2D elastic-plastic flows with the hypo-elastic constitutive model and von Mises' yielding condition. First, we develop a novel HLLC-type Riemann solver with elastic and plastic waves (HLLCEP) for 2D elastic-plastic flows. Then, we present a two-directional momentum conservative method to determine the moving speed of grid vertexes. Moreover, we introduce a special symmetry-preserving second-order reconstruction method for scalars, vectors or tensors in order to keep the good symmetric property of the proposed second-order scheme. Finally, a second-order cell-centered Lagrangian scheme, based on the developed Riemann solver (HLLCEP) and the finite volume method framework, is constructed. A number of numerical tests have been carried out, and the numerical results show that the proposed scheme reaches the second-order accuracy for problems with smooth solutions, and is essentially non-oscillatory, and appears to be convergent and symmetric. Moreover, the current HLLCEP Riemann solver is more efficient than the FRRSE solver developed in [11].