A cell-centered discontinuous Galerkin multi-material arbitrary Lagrangian-Eulerian method in axisymmetric geometry

In this paper, a cell-centered discontinuous Galerkin (DG) multi-material arbitrary Lagrangian-Eulerian (MMALE) method is developed for compressible fluid dynamics in axisymmetric geometry. The MMALE method utilizes moment-of-fluid (MOF) interface reconstruction technology to simulate multi-materials of immiscible fluids. It is an ex-plicit time-marching Lagrangian plus remapping type. In the Lagrangian stage, a volume -weighted scheme of updated cell-centered discontinuous Galerkin Lagrangian method is applied to discretize the hydrodynamic equations in pure cells, and Tipton's pressure relax-ation closure model is used in mixed cells. A robust MOF interface reconstruction algorithm is used to provide the information on the material interfaces for remapping. In the rezon-ing stage, Knupp's algorithm is used for mesh smoothing. In the remapping stage, an efficient multi-material cell-intersection-based remapping method is proposed. It can be divided into four stages: polynomial reconstruction, polygon intersection, integration, and detection of problematic cells and limiting. Polygon intersection is based on the "clipping and projecting" algorithm, and detection of problematic cells depends on a troubled cell marker, and a posteriori multi-dimensional optimal order detection (MOOD) limiting strat-egy is used for limiting. Several numerical tests are given to demonstrate the robustness and accuracy of the method.(c) 2022 Elsevier Inc. All rights reserved.