Shock capturing for a high-order ALE discontinuous Galerkin method with applications to fluid flows in time-dependent domains

跨音速 间断伽辽金法 计算机科学 自适应网格优化 翼型 稳健性(进化) 有限体积法 流固耦合 应用数学 有限元法 算法 数学优化 数学 空气动力学 计算科学 物理 机械 生物化学 化学 基因 热力学
作者
Min Gao,Pascal Mossier,Claus‐Dieter Munz
出处
期刊:Computers & Fluids [Elsevier BV]
卷期号:269: 106124-106124
标识
DOI:10.1016/j.compfluid.2023.106124
摘要

In recent decades, the arbitrary Lagrangian–Eulerian (ALE) approach has been one of the most popular choices to deal with the fluid flows having moving boundaries. The ALE finite volume (FV) method is well-known for its capability of shock capturing. Several ALE discontinuous Galerkin (DG) methods are developed to fully explore the advantages of high-order methods, especially in complex flows. The DG scheme is highly efficient and has high resolution in smooth parts of the flow while the FV scheme has advantage on the robustness against shocks. In this paper, we present a novel algorithm to combine both the ALE FV and ALE DG methods into one stable and efficient hybrid approach. The main challenge for a mixed ALE FV method and ALE DG method is to reduce the inconsistency between both discretizations. Of particular concern are the same mesh velocity distribution between DG and FV elements and a continuous mesh velocity at the coupling interfaces. Since the computational efficiency of the proposed algorithm is of major concern, performance aspects will be considered during the construction of the scheme. To investigate the accuracy of the new scheme, several benchmark test cases with prescribed movements are included. Afterwards, the algorithm is applied to more general and complex scenarios to show its ability to cope with complex setups. In our paper, the scheme is implemented into a loosely-coupled fluid–structure interaction (FSI) framework. With a shock-driven cylinder movement in a channel flow and a transonic flow-induced airfoil vibration, we demonstrate our method for FSI applications.
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