Generalized coordinate transformation and gas-kinetic scheme

Abstract

Under a generalized coordinate transformation with inclusion of both mesh velocity and acceleration, the gas-kinetic equation is transformed from a physical space to a computational space. With the WENO reconstruction, a high-order moving-mesh multidimensional gas-kinetic method, with inclusion of both normal and tangential derivatives of macroscopic flow variables, is constructed. High-order accurate Navier–Stokes solutions are obtained in the current scheme by integrating the numerical fluxes along a cell interface and over a whole time step, without using the conventional Gaussian point integration for spatial accuracy and Runge–Kutta method for temporal accuracy. For the first time, the mesh acceleration has been explicitly accounted for in the flux evaluation. Under the generalized coordinate transformation, a three-dimensional moving-mesh gas-kinetic scheme has been constructed as well. The importance of multi-dimensionality in the flux evaluation and mesh movement is illustrated through numerical tests.