A unified moving grid gas-kinetic method in Eulerian space for viscous flow computation

Under a generalized coordinate transformation with arbitrary grid velocity, the gas-kinetic BGK equation is reformulated in a moving frame of reference. Then, a unified conservative gas-kinetic scheme is developed for the viscous flow computation in the moving grid system in the Eulerian space. Due to the coupling between the grid velocity and the overall solution algorithm, the Eulerian and Lagrangian methods become two limiting cases in the current gas-kinetic method. A fully conservative formulation can be obtained even in the Lagrangian limit. The moving grid method extends the applicable regime of the gas-kinetic scheme to the flows with free surface or moving boundaries, such as dam break problem and airfoil oscillations. In order to further increase the robustness of the moving grid method, similar to the arbitrary Lagrangian–Eulerian (ALE) method, a conservative adaptive grid technique is also implemented in the current method to redistribute the mesh concentration to the rapid variational flow region and remedy the distorted moving mesh due to the coupling between grid velocity and fluid speed. Many numerical examples from incompressible flow to the supersonic shock interaction are presented. The test cases verify the accuracy and robustness of the unified moving grid gas-kinetic method.