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In this paper we present a genuinely two-dimensional HLLC Riemann solver. Onlogically rectangular meshes, it accepts four input states that come togetherat an edge and outputs the multi-dimensionally upwinded fluxes in bothdirections. This work builds on, and improves, our prior work ontwo-dimensional HLL Riemann solvers. The HLL Riemann solver presented hereachieves its stabilization by introducing a constant state in the region ofstrong interaction, where four one-dimensional Riemann problems interactvigorously with one another. A robust version of the HLL Riemann solver ispresented here along with a strategy for introducing sub-structure in thestrongly-interacting state. Introducing sub-structure turns the two-dimensionalHLL Riemann solver into a two-dimensional HLLC Riemann solver. Thesub-structure that we introduce represents a contact discontinuity which can beoriented in any direction relative to the mesh.  The Riemann solver presented here is general and can work with any system ofconservation laws. We also present a second order accurate Godunov scheme thatworks in three dimensions and is entirely based on the present multidimensionalHLLC Riemann solver technology. The methods presented are cost-competitive withtraditional higher order Godunov schemes.

A Two-dimensional HLLC Riemann Solver for Conservation Laws : Application to Euler and MHD Flows