A multi-dimensional high-order DG-ALE method based on gas-kinetic theory with application to oscillating bodies

This paper presents a multi‐dimensional high‐order discontinuous Galerkin (DG) method in an arbitrary Lagrangian‐Eulerian (ALE) formulation to simulate flows over variable domains with moving and deforming meshes. It is an extension of the gas‐kinetic DG method proposed by the authors for static domains (X. Ren et al., A multi‐dimensional high‐order discontinuous Galerkin method based on gas kinetic theory for viscous flow computations, A gas kinetic evolution model is adopted for both inviscid and viscous flux evaluations and the flux integration over a moving surface in space and time. Different from the earlier ALE‐type gas kinetic method with piecewise constant mesh velocity at each cell interface within each time step, the mesh velocity variation inside a cell and the mesh velocity change along a cell interface have been accounted for in the finite element framework, which make the method be applicable for any kind of mesh movement, such as translation, rotation and deformation, and improve the accuracy of the scheme in the oscillating airfoil calculations. The geometric conservation law (GCL) is precisely imposed due to its high order dynamic evolution model. The numerical accuracy can be maintained even for a largely moving or deforming mesh. Several test cases related to the oscillatory pitching and plunging airfoils are presented to demonstrate the performance of the DG‐ALE method.