High-order gas kinetic flux solver with TENO-THINC scheme for compressible flows

Although gas kinetic schemes (GKS) have been widely used as a potent tool for simulating compressible flows, they exhibit numerous drawbacks. Since most GKS are constructed based on the Maxwellian distribution function or its equivalent, the theoretical derivation and flux expression are often extremely complicated, which may result in lower calculation efficiency compared to traditional methods in computational fluid dynamics. In this paper, a circular function-based gas kinetic flux solver (C-GKFS) combined with a hybrid targeted essentially non-oscillatory-tangent of hyperbola for INterface capturing (TENO-THINC) scheme is presented for simulating two-dimensional compressible flows. The C-GKFS, which simplifies the Maxwellian distribution function into a circular function, significantly enhances computing efficiency. The TENO-THINC scheme, which combines the standard TENO scheme for smooth regions with the THINC scheme for non-smooth discontinuities, preserves low dissipation for smooth flow while effectively resolves the profile of jump for shock and contact waves. As a result, a simple high-order C-GKFS is obtained, which reduces complexity to facilitate practical engineering applications. Some benchmark problems are simulated, and good agreement can be obtained compared with reference data, which demonstrates that the TENO-THINC based C-GKFS achieves the desired accuracy and performs significantly better than the standard TENO scheme.