Path Conservative WENO Schemes and Riemann Solvers for Continuum Mechanics

摘要

We present on novel complete Riemann solvers for a unified first order hyperbolic formulation of continuum mechanics [7], [8], which is able to describe fluids and solids at the same time. In particular, we have considered a generalization of the Riemann solver of Osher and of the HLLEM Riemann solver, see [2], [6]. Since the governing PDE system also contains non-conservative products, the use of so-called path-conservative schemes becomes necessary, in order to give a sense to the nonconservative terms in the framework of weak solutions. The implementation and testing of the new Riemann solvers was successful and the complete Riemann solvers clearly behave better than standard local Lax-Friedrichs-type or Rusanov-type Riemann solvers.