On the High - Order Multidimensional Gas - Kinetic Scheme

The newly developed high-order-accurate multidimensional gas-kinetic scheme is further investigated, including the benefit of the consideration of tangential slopes in the flux function at a cell interface, and the application of the scheme in turbulence simulation. The present study shows that in despite of increasing of computational cost, the multidimensional scheme can evidently improve the accuracy when compared to the directional splitting one. The numerical simulation of the compressible turbulence with the high-order multidimensional gas-kinetic scheme shows better performance than the existing second-order gas-kinetic method.