Arbitrary Lagrangian-Eulerian-type discrete unified gas kinetic scheme for low-speed continuum and rarefied flow simulations with moving boundaries.

Abstract

In this paper, the original discrete unified gas kinetic scheme (DUGKS) is extended to the arbitrary Lagrangian-Eulerian (ALE) framework to enable simulation of low-speed continuum and rarefied flows with moving boundaries. For the proposed ALE-type DUGKS, the mesh motion velocity is introduced in the Boltzmann-BGK equation and a remapping-free scheme is used to discretize the governing equation. Under this coupling framework, the complex rezoning and remapping phases implemented in the traditional ALE method are avoided. In some application areas, large discretization errors are introduced in the simulation if the geometric conservation law (GCL) is not guaranteed. Therefore, three GCL-compliant approaches are discussed, and a uniform flow test case is conducted to validate these schemes. Further, to illustrate the performance of the proposed method, four test cases are simulated, including the continuum flow around an oscillating circular cylinder, the continuum flow around a pitching NACA0012 airfoil, a moving piston driven by a rarefied gas, and the rarefied flow caused by a plate oscillating in the normal direction. Finally, an extended test case considering the rarefied flow over an oscillating circular cylinder is also studied, as this condition is not sufficiently researched. Consistent and good results obtained from the above test cases demonstrate the capability of the proposed ALE-type DUGKS to simulate moving boundary problems in different flow regimes.