High-order gas kinetic flux solver for viscous compressible flow simulations

Although the gas kinetic schemes (GKS) have emerged as one of the powerful tools for simulating compressible flows, they exhibit several shortcomings. Since the local solution of continuous Boltzmann equation with the Maxwellian distribution function is used to calculate the numerical fluxes at the cell interface, the flux expression in GKS is usually more complicated. In this paper, a high-order simplified gas kinetic flux solver (GKFS) is presented for simulating two-dimensional compressible flows. Circular function-based GKFS (C-GKFS), which simplifies the Maxwellian distribution function into the circular function, combined with an improved weighted essentially non-oscillatory (WENO-Z) scheme is applied to capture more details of the flow fields with fewer grids. As a result, a simple high-order accurate C-GKFS is obtained, which improves the computing efficiency and reduce its complexity to facilitate the practical application of engineering. A series of benchmark-test problems are simulated and good agreement can be obtained compared with the references, which demonstrate that the high-order C-GKFS can achieve the desired accuracy.