A simple distribution function-based gas-kinetic scheme for simulation of viscous incompressible and compressible flows

摘要: In this work, a simple distribution function-based gas-kinetic scheme for simulation of viscous flows is presented. The work applies the finite volume method to discretize governing differential equations, and inviscid fluxes at cell interface are evaluated simultaneously by local reconstruction solution continuous Boltzmann equation. Differently from conventional [13-15], in present Maxwellian function simplified function, integrals infinity domain phase space reduced around circle. As consequence, computational efficiency greatly improved. Since defined on circle, simplicity, it termed as circular hereafter. extension our previous [20], where presented simulate flows. Only equilibrium considered [20]. To solve flows, non-equilibrium part density has be considered. One major contributions way compute function. It can calculated difference functions its surrounding point. result, formulations computing conservative flow variables given explicitly. solver both incompressible compressible validate proposed new scheme, several simulated. Numerical results showed that provide accurate numerical with same cost needed Navier-Stokes solver.