A cell-centered discontinuous Galerkin finite element MMALE method

A 2D cell-centered multi-material arbitrary Lagrangian-Eulerian method is presented for compressible multi-material fluid dynamics. In the Lagrangian phase, a cell-centered discontinuous Galerkin method is used to solve the hydrodynamic equations. To simplify the discrete form of these equations, an appropriate basis function with zero material derivative is selected. For mixed cells, the Tipton pressure relaxation model and the isoparametric coordinate method are used respectively to update the physical quantity and the centroids of materials. In addition, a robust MOF method is used for interface reconstruction. In the remapping phase, a second-order integral conservative remapping method is proposed. This method is based on polygon intersection and can be divided into four parts, i.e, the polynomial reconstruction, the polygon intersection, the integration, and a posteriori correction. Specifically, the polygon intersection is equipped with a "clipping and projecting" algorithm. And the posteriori correction is based on Multi-dimensional Optimal Order Detection restriction strategy with some modifications to facilitate the multi-material calculation. This correction is employed to detect problematic cells and further suppress non-physical numerical oscillations in these cells. Numerical examples show that the proposed method is of second-order accuracy and has a good robustness.