Arbitrary Lagrangian-Eulerian-type conserved discrete unified gas kinetic scheme for the simulations of transonic continuum and rarefied gas flows with moving boundaries

Abstract

In this paper, an arbitrary Lagrangian-Eulerian (ALE) framework is incorporated into the conserved discrete unified gas-kinetic scheme (CDUGKS) to solve the transonic continuum and rarefied gas flows with moving boundary. This is a continuation of our earlier work [Y. Wang et al., Phys. Rev. E, 100(6), 063310 (2019)]. Compared to the original low-speed ALE-DUGKS, in which only the governing equation of the distribution function is solved, the mesh motion velocity is introduced in the proposed ALE-CDUGKS for updating both the distribution function and the conservative flow variables. For a flow in the continuum regime, the potential energy double-distribution-functions framework and the circle equilibrium distribution function model are incorporated for inviscid and viscous flows. In the rarefied flow regime, the technique of unstructured velocity-space mesh is introduced to decrease the total number of discrete particle-velocity points and reduce the computational load. In addition, a loosely-coupled algorithm for simulating the fluid-structure interaction problem (airfoil flutter) is also presented. As a result, under this unified framework based on the distribution function, the numerical simulations have relatively high computational efficiency for flows in both continuum and rarefied regimes. A series of flows around a stationary or moving airfoil in the continuum regime is simulated, and a plunging airfoil in rarefied gas flow is also studied. The consistent and good results obtained from the above test cases demonstrate the capability of the proposed ALE-CDUGKS for solving the compressible moving boundary problems with the rarefied gas effect.