Efficient Wall-Modeled High-Order Compact Gas-Kinetic Scheme for Compressible Turbulent Flows

Abstract: Scale-resolving simulations of wall-bounded turbulent flows remain prohibitively expensive at high Reynolds numbers, owing to the stringent near-wall resolution requirements. High-order compact gas-kinetic schemes (CGKS) are accurate, robust, and efficient for compressible flows, making them an attractive foundation for reducing this cost. Building on the fifth-order scheme CGKS-5th, we develop a wall-modeled CGKS framework that alleviates the near-wall resolution burden through a pressure-gradient-based non-equilibrium wall model while preserving the resolving power of the outer solver. CGKS-5th resolves the outer flow and supplies the wall model with data at the exchange location. On coarse near-wall meshes, the wall model reconstructs the under-resolved viscous wall stress, while CGKS-5th provides the inviscid wall flux directly; the two combine to form the wall momentum flux. To capture non-equilibrium effects in adverse-pressure-gradient and separated regions, the wall model retains a pressure-gradient source term together with a pressure-gradient-corrected near-wall damping function. We assess the framework on two distinct flows: bluff-body separation past a circular cylinder, and a shock-induced separation bubble on the transonic RAE 2822 airfoil, using near-wall meshes far coarser than wall-resolved simulations require. For the RAE 2822 case, this corresponds to a twentyfold coarsening in the wallnormal direction, with comparable coarsening in other directions. In both cases, the wall-modeled CGKS-5th reproduces the separated flow structures and markedly improves near-wall predictions over its wall-model-free counterpart, most notably the skin-friction coefficient. The framework thus delivers accurate predictions of these separated flows at substantially reduced near-wall cost, while its lightweight coupling adds less than 1% runtime overhead in a multi-GPU implementation.