HLLEPJ and HLLCEPJ Riemann solvers for the Wilkins model of elastoplasticity.

This paper presents three Riemann solvers for the Wilkins model of hypoelasticity with the Jaumann derivative correction. The solvers are developed as extensions of the HLL and HLLC Riemann solvers for the Euler hydrodynamic model and differ in the number of waves considered (two-wave HLLEPJ Riemann solver, three-wave HLLCEPJ Riemann solver and five-wave HLLCEPJ Riemann solver). The discontinuous solution of the Wilkins system of equations is obtained using generalized Rankine-Hugoniot relations developed on the basis of the path-conservative DLM approach. A special choice of the path in the phase space allows to avoid any iterative processes in the solver construction. The proposed Riemann solvers are implicated in the first order Finite Volume numerical scheme for testing on the set of 1D, 2D and 3D problems of elastoplastic flows. • The non-iterative solvers differ in the number of waves considered - two, three and five waves are considered in the Riemann problem approximation. • The discontinuous solution of the Wilkins system of equations is obtained using generalized Rankine-Hugoniot relations developed on the basis of the path-conservative DLM approach. • The proposed solvers are tested by implication in the first order Finite Volume numerical scheme for numerical calculation of several test problems. [ABSTRACT FROM AUTHOR]