...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Journal of Computational Physics >A sparse and high-order accurate line-based discontinuous galerkin method for unstructured meshes
【24h】

A sparse and high-order accurate line-based discontinuous galerkin method for unstructured meshes

机译：非结构化网格的稀疏高阶精确基于线的不连续伽勒金方法

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

We present a new line-based discontinuous Galerkin (DG) discretization scheme for firstand second-order systems of partial differential equations. The scheme is based on fully unstructured meshes of quadrilateral or hexahedral elements, and it is closely related to the standard nodal DG scheme as well as several of its variants such as the collocationbased DG spectral element method (DGSEM) or the spectral difference (SD) method. However, our motivation is to maximize the sparsity of the Jacobian matrices, since this directly translates into higher performance in particular for implicit solvers, while maintaining many of the good properties of the DG scheme. To achieve this, our scheme is based on applying one-dimensional DG solvers along each coordinate direction in a reference element. This reduces the number of connectivities drastically, since the scheme only connects each node to a line of nodes along each direction, as opposed to the standard DG method which connects all nodes inside the element and many nodes in the neighboring ones. The resulting scheme is similar to a collocation scheme, but it uses fully consistent integration along each 1-D coordinate direction which results in different properties for nonlinear problems and curved elements. Also, the scheme uses solution points along each element face, which further reduces the number of connections with the neighboring elements. Second-order terms are handled by an LDG-type approach, with an upwind/downwind flux function based on a switch function at each element face. We demonstrate the accuracy of the method and compare it to the standard nodal DG method for problems including Poisson's equation, Euler's equations of gas dynamics, and both the steady-state and the transient compressible Navier-Stokes equations. We also show how to integrate the Navier-Stokes equations using implicit schemes and Newton-Krylov solvers, without impairing the high sparsity of the matrices.
机译：我们为偏微分方程的一阶和二阶系统提出了一种新的基于行的不连续Galerkin（DG）离散化方案。该方案基于四边形或六面体元素的完全非结构化网格，并且与标准节点DG方案及其若干变体（例如基于并置的DG光谱元素方法（DGSEM）或光谱差（SD））密切相关。方法。但是，我们的动机是使Jacobian矩阵的稀疏性最大化，因为这直接转化为更高的性能，尤其是对于隐式求解器，同时保持了DG方案的许多优良特性。为此，我们的方案基于在参考元素中沿每个坐标方向应用一维DG求解器。与标准DG方法不同，该方法仅将每个节点沿每个方向连接到一行节点，这大大减少了连接数，而标准DG方法将元素内的所有节点与相邻节点中的许多节点连接起来。生成的方案类似于并置方案，但是它沿每个1-D坐标方向使用完全一致的积分，这导致非线性问题和弯曲元素具有不同的属性。而且，该方案使用沿每个元素面的求解点，这进一步减少了与相邻元素的连接数。二阶项由LDG类型的方法处理，在每个元素面具有基于开关函数的上/下风通量函数。我们证明了该方法的准确性，并将其与标准节点DG方法进行了比较，以解决包括泊松方程，气体动力学的欧拉方程以及稳态和瞬态可压缩Navier-Stokes方程在内的问题。我们还展示了如何使用隐式方案和Newton-Krylov求解器对Navier-Stokes方程进行积分，而又不损害矩阵的稀疏性。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号