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 arbitrary Lagrangian-Eulerian (ALE) framework for simulating the low-speed continuum and rarefied flows with moving boundaries. For ALE method, the mesh moving velocity is introduced into the Boltzmann-BGK equation. The remapping-free scheme is adopted to develop the present ALE-type DUGKS, which avoids the complex rezoning and remapping process in traditional ALE method. As in some application areas, the large discretization errors will be introduced into the simulation if the geometric conservation is not guaranteed. Three compliant approaches of the geometric conservation law (GCL) are discussed and a uniform flow test case is conducted to validate these schemes. To illustrate the performance of present ALE-type DUGKS, four test cases are carried out. Two of them are the continuum flow cases, which are the flows around the oscillating circular cylinder and the pitching NACA0012 airfoil, respectively. Others are the rarefied flow cases, one is the moving piston driven by the rarefied gas, another is the flow caused by the plate oscillating in its normal direction. The results of all test cases are in good agreement with the other numerical and/or experimental results, demonstrating the capability of present ALE-type DUGKS to cope with the moving boundary problems at

Investigation of nonlinear squeeze-film damping involving rarefied gas effect in micro-electro-mechanical-systems

“…The original DUGKS proposed by Guo et al [20] and the ALE-DUGKS proposed by Wang et al [28] are the numerical schemes based on the Boltzmann model equation. In this work, the Boltzmann-BGK equation is used, which can be expressed as…”

“…where n is the time level, ∆t = t n+1 − t n is the time step, x b is the center of cell interface, and k is the total number of cell interfaces. Under the ALE framework, as the geometrical information of a grid cell changes temporally during the simulation, the cell volumes V n+1, * and V n, * at n and n + 1 time levels, the moving velocity of cell interface v n+1/2 b at n + 1/2 time, the outward unit normal vector n * b , and the area of cell interface S * b must be calculated by the discretized geometric conservation law (DGCL) [28,44], where superscript * means that the values of variables at corresponding times maybe not equal to the real values of variables at those times. In this study, the DGCL scheme-2 presented in Ref.…”

“…Currently, some improved and enhanced schemes based on the DUGKS also have been developed [25,26,27]. And, Wang et al [28] proposed an arbitrary Lagrangian-Eulerian-type DUGKS for solving the moving boundary problems in continuum and rarefied gas flows. So, the original DUGKS and ALE-DUGKS are the promising numerical schemes for studying the micro-flows and the SFD phenomena in MEMS.…”

Moving Boundaries in Common Envelope Evolution

“…For example, in modeling the flow around an airfoil the edges of the simulation box can be treated as inflow or outflow boundaries and the airfoil itself as a reflective boundary, which allows no matter to pass through it. Indeed, Wan & Zhong (2019) use a 2-D ALE scheme with moving boundaries to model a pitching NACA 0012 airfoil. Such schemes are common in fields such as aerodynamics, but also have interesting and useful applications in astrophysics.…”

GKS and UGKS for High-Speed Flows

“…Thus, the computational cost and memory consumption are huge in the UGKS, especially for high-speed rarefied flow simulation with discrete points to cover a six-dimensional physical and velocity space. Therefore, many numerical techniques have been developed and implemented in the UGKS to increase the computational efficiency and reduce memory cost, such as unstructured mesh computation [44,45], moving grids [46,47], velocity space adaptation [47,48], memory reduction [49,50], wave-particle adaptation [51,52], implicit algorithms [53][54][55][56], and fur-ther simplification and modification [57,58]. With these treatments, the UGKS becomes a powerful tool to solve multiscale problems, and shows great advantages in the simulations of high-speed and non-equilibrium flow with a large variation of local Knudsen number in a single computation.…”