Finite Difference Implementation of a High-order Space-Time Coupled Compact Gas-Kinetic Scheme

Abstract: This study presents a high-order compact finite difference gas-kinetic scheme (FD-CGKS) that introduces a novel spatial discretization strategy for the efficient implementation of space-time coupled high-order schemes on structured grids. A conservative nonlinear compact discretization is achieved by formulating numerical fluxes from physical fluxes at both nodal and interfacial locations. To simplify the multidimensional spatial reconstruction required for the GKS flux evaluation, we propose a dual-grid approach that updates conservative variables on both a primary grid and an identical dual grid, offset by half the mesh spacing. By leveraging the time-accurate interface solutions from the gas-kinetic evolution model, the scheme explicitly updates averaged spatial derivatives between virtual interfaces, naturally enabling compact high-order reconstruction. Furthermore, a nonlinear GENO method is incorporated to capture flow discontinuities with high resolution and robustness, effectively suppressing spurious oscillations. The proposed framework, which also offers new perspectives for designing schemes based on space-time decoupled Riemann solvers, is systematically validated. Comprehensive benchmark computations of inviscid and viscous flows demonstrate the scheme's high accuracy in resolving a wide spectrum of flow features, from smooth multiscale structures to strong shock discontinuities.