A HLLC scheme for nonconservative hyperbolic problems. Application to turbidity currents with sediment transport.

Abstract

This paper focuses on the generalization of the HLLC Riemann solver for nonconservative problems. First, the general ideas of the extension of the HLLC solvers for nonconservative systems are discussed. Then, two particular HLLC solvers are described for a turbidity current model with sediment transport. Some results concerning the positivity of the corresponding schemes are presented. Several numerical tests are performed to compare the two HLLC solvers among them and with a Roe method.