An adaptive grid method for two-dimensional viscous flows

This paper extends the gas-kinetic BGK-NS scheme to an adaptive grid for the viscous flow simulations. The grid movement and adaptation is controlled by a monitor function which may depend on velocity gradient or other flow variables, such as density or pressure. For the viscous flow computation, the use of adaptive mesh much improves the efficiency and accuracy of the method in comparison with the methods with static mesh points. The current method is an accurate and efficient method for the viscous flow computation, where the grid points can be easily moved and concentrated on the regions with large velocity and density gradients, such as the boundary layer and multi-material interface. Many numerical examples validate the current approach for the viscous flow simulations.