论文标题
在任意拉格朗日 - 尤拉利亚公式中，重建的不连续的galerkin方法用于可压缩流
Reconstructed discontinuous Galerkin method for compressible flows in arbitrary Lagrangian-Eulerian formulation
论文作者
论文摘要
我们在任意拉格朗日 - 欧拉（ALE）配方中提出了一种高阶准确的不连续的盖尔金（RDG）方法，用于求解具有非结构化的弯曲网格的移动和变形域上的二维压缩流。使用的泰勒基础函数是在时间依赖性域上定义的，在该结构域上也进行了集成和计算。用于时间整合的第三阶ESDIRK3方案。通过修改高斯正交点离散方程的右侧的网格速度项来满足几何保护定律（GCL）。为了避免移动边界附近过度的失真和无效的元素，我们使用径向基函数（RBF）插值方法将边界节点的网格运动传播到网格内部。执行了几个数值示例，以验证设计的空间和时间序列的准确性，并证明处理RDG-ALE方法的移动边界问题的能力。
We present a high-order accurate reconstructed discontinuous Galerkin (rDG) method in arbitrary Lagrangian-Eulerian (ALE) formulation, for solving two-dimensional compressible flows on moving and deforming domains with unstructured curved meshes. The Taylor basis functions in use are defined on the time-dependent domain, on which also the integration and computations are performed. A third order ESDIRK3 scheme is employed for the temporal integration. The Geometric Conservation Law (GCL) is satisfied by modifying the grid velocity terms on the right-hand side of the discretized equations at Gauss quadrature points. To avoid excessive distortion and invalid elements near the moving boundary, we use the radial basis function (RBF) interpolation method for propagating the mesh motion of the boundary nodes to the interior of the mesh. Several numerical examples are performed to verify the designed spatial and temporal orders of accuracy, and to demonstrate the ability of handling moving boundary problems of the rDG-ALE method.
