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

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. (c) 2022 Elsevier Inc. All rights reserved.

Automated summary

In this paper, an arbitrary Lagrangian-Eulerian (ALE) framework is introduced into the conserved discrete unified gas-kinetic scheme (CDUGKS) to solve transonic continuum and rarefied gas flows with moving boundary. The proposed ALE-CDUGKS updates both the distribution function and the conservative flow variables, and it shows high computational efficiency for flows in both continuum and rarefied regimes. The method incorporates the potential energy double-distribution-functions framework and the circle equilibrium distribution function model for continuum flows, and introduces unstructured velocity-space mesh technique for rarefied flows to reduce computational load. The capability of the proposed ALE-CDUGKS for solving compressible moving boundary problems with rarefied gas effect is demonstrated through simulations of various test cases.