Development of a moving reference frame-based gas-kinetic BGK scheme for viscous flows around arbitrarily moving bodies

In this paper, a moving reference frame-based gas-kinetic BGK (MRF–BGK) scheme is developed for simulation of viscous flows around arbitrarily moving bodies. Different from most of existing gas-kinetic schemes, the BGK model is now constructed in a general moving reference frame. Due to the non-inertial effects, there will be an additional acceleration term in the Boltzmann equation, which should be carefully defined in order to correctly recover the concerned Navier–Stokes (N–S) equations. This recovery actually serves as a basis for developing the present method. Within the finite volume framework, the BGK model with the inclusion of the acceleration term is locally solved and the numerical fluxes at the cell interface can be evaluated. Through this way, the source (acceleration) term effects can be naturally included into the gas evolution process and the resulting fluxes. Considering that explicit BGK schemes may show low efficiency for certain unsteady applications where the physical time scales are significantly larger than the spatial scales, the dual time-stepping approach together with an implicit BGK scheme is employed. Numerical tests show that the developed MRF–BGK scheme can be well applied for several incompressible and compressible viscous flows. The accuracy is shown to be comparable to the moving grid BGK method, however the mesh movement is avoided in the present method. Also as compared with the immersed boundary BGK method, it is more efficient to deal with high-Reynolds number flows.