A Second-Order Cell-Centered Lagrangian Method for Two-Dimensional Elastic-Plastic Flows (Communications in Computational Physics, 2017)
For 2D elastic-plastic flows with the hypo-elastic constitutive model and vonMises' yielding condition, the non-conservative character of the hypo-elastic constitutivemodel and the von Mises' yielding condition make the construction of the solutionto the Riemann problem a challenging task. In this paper, we first analyze thewave structure of the Riemann problem and develop accordingly a Four-Rarefactionwave approximate Riemann Solver with Elastic waves (FRRSE). In the constructionof FRRSE one needs to use an iterative method. A direct iteration procedure for fourvariables is complex and computationally expensive. In order to simplify the solutionprocedure we develop an iteration based on two nested iterations upon two variables,and our iteration method is simple in implementation and efficient. Based on FRRSE asa building block, we propose a 2nd-order cell-centered Lagrangian numerical scheme.Numerical results with smooth solutions show that the scheme is of second-order accuracy.Moreover, a number of numerical experiments with shock and rarefaction wavesdemonstrate the scheme is essentially non-oscillatory and appears to be convergent.For shock waves the present scheme has comparable accuracy to that of the schemedeveloped by Maire et al., while it is more accurate in resolving rarefaction waves.