论文标题
2D不可压缩的Navier-Stokes方程的交错网格上的半显微高阶时空方程
A semi-implicit high-order space-time scheme on staggered meshes for the 2D incompressible Navier-Stokes equations
论文作者
论文摘要
提出了一种新的高阶准确的半平时时间不连续的盖尔金方法，以模拟二维域上的粘性不可压缩流。设计的方案是任意的Lagrangian Eulerian类型，适用于固定和移动网格的工作。在我们的时空公式中，通过用分段时空多项式表达数值解决方案，通过简单有效的PICARD迭代方法实现了任意的高度准确性。对于双网格，基本函数由四边形内两个亚三角形的连续分段多项式组成：这允许构建不含正交的方案，从而产生非常有效的算法。一些数值示例确认所提出的方法的表现优于现有方法。
A new high order accurate semi-implicit space-time Discontinuous Galerkin method on staggered grids, for the simulation of viscous incompressible flows on two-dimensional domains is presented. The designed scheme is of the Arbitrary Lagrangian Eulerian type, which is suitable to work on fixed as well as on moving meshes. In our space-time formulation, by expressing the numerical solution in terms of piecewise space-time polynomials, an arbitrary high order of accuracy in time is achieved through a simple and efficient method of Picard iterations. For the dual mesh, the basis functions consist in the union of continuous piecewise polynomials on the two subtriangles within the quadrilaterals: this allows the construction of a quadrature-free scheme, resulting in a very efficient algorithm. Some numerical examples confirm that the proposed method outperforms existing ones.
