Hybridization of compact and WENO schemes for simulation of turbulent flows with shocks

Computation of flow through shock waves was extremely difficult to handle, as shocks present sharp changes in flow variables like density, pressure and velocity. One could have handled such changes by using a very fine mesh that could capture these gradients, but this would have led to higher computational costs. The use of shock capturing schemes has been a useful innovation towards handling flow through shocks while still keeping the mesh relatively coarse. These schemes, namely ENO, WENO etc., smear the shock over a few points in the computational domain, in order to better handle the near infinite gradients. This smearing is a result of numerical (artificial) dissipation added by these schemes. On the other hand, while simulating high speed turbulent flows, this artificial dissipation adds to the natural turbulent dissipation and dissipates the turbulence excessively. Consequently, the accuracy of the simulation results at areas away from shocks, suffers. To accurately capture both natural turbulence and shocks, a hybridization between a non-dissipative and a dissipative scheme is devised. A sixth order basal compact scheme is hybridized with several variations of the WENO schemes. The switch between the compact and WENO scheme is controlled by a shock detector. The resulting hybrids are tested on well-known benchmark problems and validated by comparison with results from using a WENO scheme on a fine grid