Conservative Hybrid Compact-WENO Schemes for Shock-Turbulence Interaction

In the present paper an efficient hybrid compact-WENO scheme is proposed to obtain high resolution in shock-turbulence interaction problems. The algorithm is based on a fifth-order compact upwind algorithm in conservation form to solve for the smooth part of the flow field, which is coupled with a high-resolution weighted essentially nonoscillatory (WENO) scheme to capture the discontinuities. The derivation of the compact scheme is discussed in detail, and a stability study of the full discretization is included. The performance of the numerical algorithm has been assessed by performing preliminary simulations on benchmark problems, such as the interaction of a shock wave with entropy and vortical disturbances. The algorithm here developed is proven to have better resolution properties than standard WENO schemes and hybrid compact-ENO schemes as well, at a lower computational cost. In addition, the application to more realistic shock-turbulence interaction problems is discussed.