Finite volume method

Riemann solver

Plasticity

Materials science

Applied mathematics

Riemann problem

Mathematical optimization

Solver

Classical mechanics

Thermodynamics

Physics

Riemann hypothesis

Mathematics

Mathematical analysis

Geometry

Composite material

Mechanics

Computers & Fluids

A multi-material HLLC-type approximate Riemann solver with both elastic and plastic waves (MHLLCEP) is constructed for 1D elastic-plastic flows with the hypo-elastic model and the von Mises yielding condition. Although Cheng in 2016 [1] introduced a HLLC Riemann solver with elastic waves (HLLCE) for 1D elastic-plastic flows, Cheng assumed that pressure is continuous across a contact wave. This assumption may lead to numerical errors, especially for multi-material elastic-plastic flows. In our MHLLCEP, this assumption is not used again. Correspondingly, the errors introduced by the assumption are deleted, describing and evaluating the plastic waves are more accurate than that in the HLLCE. For the multi-material system, in this paper, a ghost cell method is used to eliminate the numerical oscillations and keep a high-order spatial reconstruction across the interface. Based on the MHLLCEP, combining with the third-order WENO reconstruction method and the third-order Runge–Kutta method in time, a high-order cell-centered Lagrangian scheme for 1D multi-material elastic-plastic flows is built in this paper. A number of numerical experiments are carried out. Numerical experiments show that the third-order scheme is robust, essentially non-oscillatory and, as suggested by numerical experiments, may also be convergent. Moreover, for multi-material elastic-plastic flows, the scheme with the MHLLCEP is more accurate and reasonable in resolving the multi-material interface than the scheme with the HLLCE.

A multi-material HLLC Riemann solver with both elastic and plastic waves for 1D elastic-plastic flows