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

Abstract

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 explicit 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 relaxation 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 rezoning 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 strategy is used for limiting. Several numerical tests are given to demonstrate the robustness and accuracy of the method.