A High-Order Cell-Centered Discontinuous Galerkin Multi-Material Arbitrary Lagrangian-Eulerian Method (Communications in Computational Physics, 2020)
In this paper, a high-order cell-centered discontinuous Galerkin (DG) multi-material arbitrary Lagrangian-Eulerian (MMALE) method is developed for compressible fluid dynamics. The MMALE method utilizes moment-of-fluid (MOF) interfacereconstruction technology to simulate multi-materials of immiscible fluids. It is anexplicit time-marching Lagrangian plus remap type. In the Lagrangian phase, an updated high-order discontinuous Galerkin Lagrangian method is applied for the discretization of hydrodynamic equations, and Tipton's pressure relaxation closure modelis used in the mixed cells. A robust moment-of-fluid interface reconstruction algorithmis used to provide the information of the material interfaces for remapping. In the rezoning phase, Knupp's algorithm is used for mesh smoothing. For the remappingphase, a high-order accurate remapping method of the cell-intersection-based type isproposed. 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 problematiccells depends on a troubled cell marker, and a posteriori multi-dimensional optimal order detection (MOOD) limiting strategy is used for limiting. Numerical tests are givento demonstrate the robustness and accuracy of our method.
Keywords: Multi-material ALE; discontinuous Galerkin; moment-of-fluid; Tipton's pressure relaxation closure model; a posteriori MOOD limiting strategy.