A hybrid kinetic WENO scheme for compressible flow simulations

The hybrid kinetic Weighted Essentially Non-Oscillatory (WENO) scheme proposed in Int. J. Numer. Meth. Fluids 2015, 79: 290-305 is further studied in this paper. In a conventional WENO framework, flux vector splitting (FVS) techniques are usually used for the numerical flux evaluation at cell interfaces, and it is well known that the numerical dissipation of FVS methods is relatively large due to the free transfer mechanism of gas molecules, in order to reduce the dissipation in the procedure of flux calculations, a hybrid kinetic WENO scheme was introduced in the above-mentioned paper, where the 5th order scheme employing the proposed hybrid kinetic approach has been validated. In this paper, we further test the 7th order scheme using the hybrid kinetic method. It is indicated that the 7th order hybrid kinetic WENO scheme is more accurate and less dissipative than that adopting conventional FVS techniques and has a good shock-capturing capability, some examples including both one-dimensional and two-dimensional cases are presented.