一种中心型间断有限元MMALE方法

A cell-centered discontinuous Galerkin finite element MMALE method

针对多介质可压缩流体动力学问题,提出了一种单元中心型二维MMALE(Multi-Material Arbitrary Lagrangian-Eulerian)方法。在拉氏步,流体力学方程组采用中心型间断有限元方法求解。对于混合网格,采用Tipton压力松弛模型更新物理量,用等参坐标法更新物质中心点坐标。界面重构采用一种健壮的MOF(Moment of Fluid)方法。在重映步提出了基于多边形相交的二阶积分守恒重映方法。该方法分为四个部分:多项式重构、多边形相交、积分和后验校正。多边形相交使用"剪裁投影"算法,显著降低了多边形相交算法的复杂度。后验校正是基于MOOD (Multi-dimensional Optimal Order Detection)限制策略,并做了一些改动以适应多介质的计算。数值算例表明,该方法具有二阶的精度和较好的鲁棒性。

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.