Gas kinetic flux solver based finite volume weighted essentially non-oscillatory scheme for inviscid compressible flows

A high-order gas kinetic flux solver (GKFS) is presented for simulating inviscid compressible flows. The weighted essentially non-oscillatory (WENO) scheme on a uniform mesh in the finite volume formulation is combined with the circular function-based GKFS (C-GKFS) to capture more details of the flow fields with fewer grids. Different from most of the current GKFSs, which are constructed based on the Maxwellian distribution function or its equivalent form, the C-GKFS simplifies the Maxwellian distribution function into the circular function, which ensures that the Euler or Navier-Stokes equations can be recovered correctly. This improves the efficiency of the GKFS and reduces its complexity to facilitate the practical application of engineering. Several benchmark cases are simulated, and good agreement can be obtained in comparison with the references, which demonstrates that the high-order C-GKFS can achieve the desired accuracy.