Evaluation of cubic-spline based gas kinetic method for simulating compressible turbulence

In this work, we implement and examine a new flow reconstruction methodology using cubic-splines for interpolations in the gas kinetic method (GKM). We compare this version of GKM with the existing WENO based interpolation method. The comparisons are made in terms of accuracy and computational speed. We find that at low to intermediate range of Mach number (Mt < 0.7), cubic-splines based interpolations are superior in terms of reduced numerical dissipation and higher computational speed (7x faster) as compared to the WENO interpolation method.