Meshfree method based on discrete gas-kinetic scheme to simulate incompressible/compressible flows

A meshfree method based on the discrete gas-kinetic scheme (DGKS) (called meshfree-DGKS) for simulation of incompressible/compressible flows is proposed in this work. In approach, governing equations are discretized using least squares-based finite difference approach. To simulate compressible problems with discontinuities, virtual mid-points between adjacent nodes, which regarded as Riemann established. Then, concept numerical flux introduced, enables computing both and incompressible problems. The fluxes at calculated DGKS particle velocity model. corresponding components distribution functions integrated moment relations to obtain flux. meshfree-DGKS maintains advantages meshless it implemented arbitrarily distributed nodes. This breaks through limitations grid topology suitable handle complex geometries. More importantly, mid-point reconstructed local solution Boltzmann equation, can describe its physical properties well, thus easily stably capturing shock wave. addition, simultaneously calculate inviscid viscous when simulating flow problems, gives an improved algorithm consistency. Several representative examples, such tube implosion problem, couette flow, lid-driven cavity a channel backward-facing step, supersonic around ramp segment, staggered NACA0012 biplane configuration, simulated validate meshfree-DGKS.