HLLC Riemann solver based on high-order reconstruction for unsteady inviscid compressible flows

The performance of one high-resolution scheme is investigated in various unsteady, inviscid, compressible flows. In this paper, we are concerned about Harten-Lax-van Leer-Contact (HLLC) approximate Riemann solver and compare it with Roe Riemann solver. For better accuracy, fifth-order improved weighted essentially non-oscillatory (WENO) schemes are adopted to reconstruct left and right states across a cell interface. We propose that for systems the reconstruction is executed in primitive variables, instead of conservative variables. The performance of the schemes has been assessed in four typical problems. The results reveal that WENO-HLLC has the great capabilities to capture shock and contact discontinuities with high resolution.