A hybrid kinetic WGVC–WENO scheme for compressible flows

Abstract

In this paper, we propose a hybrid kinetic weighted group velocity control–weighted essentially non-oscillatory (WGVC–WENO) scheme which combines the WGVC–WENO reconstruction technique He et al. (2014) with the hybrid kinetic method proposed in Liu et al. (2015). The new scheme is based on the idea of hybridization. The hybrid kinetic method is adopted for flux calculations, and the WGVC–WENO technique is adopted for physical reconstructions. In smooth flow regions, the collision-related flux method and WGVC reconstruction technique play a leading role. The kinetic flux vector splitting (KFVS) method and WENO reconstruction technique are dominant in discontinuous regions. The third-order TVD Runge–Kutta method is used for temporal discretization. Many one-dimensional and two-dimensional numerical examples show that the new scheme has the properties of high accuracy, low dissipation, and good shock-capturing ability.