Finite volume method

Riemann solver

Applied mathematics

Riemann problem

Rarefaction (ecology)

Mathematical optimization

Solver

Classical mechanics

Geology

Paleontology

Physics

Riemann hypothesis

Mathematics

Mathematical analysis

Mechanics

Species richness

Applied Mathematics and Mechanics

A Harten-Lax-van Leer-contact (HLLC) approximate Riemann solver is built with elastic waves (HLLCE) for one-dimensional elastic-plastic flows with a hypoelastic constitutive model and the von Mises’ yielding criterion. Based on the HLLCE, a third-order cell-centered Lagrangian scheme is built for one-dimensional elastic-plastic problems. A number of numerical experiments are carried out. The numerical results show that the proposed third-order scheme achieves the desired order of accuracy. The third-order scheme is used to the numerical solution of the problems with elastic shock waves and elastic rarefaction waves. The numerical results are compared with a reference solution and the results obtained by other authors. The comparison shows that the presented high-order scheme is convergent, stable, and essentially non-oscillatory. Moreover, the HLLCE is more efficient than the two-rarefaction Riemann solver with elastic waves (TRRSE).

Harten-Lax-van Leer-contact (HLLC) approximation Riemann solver with elastic waves for one-dimensional elastic-plastic problems