An adaptive multilevel multigrid formulation for Cartesian hierarchical grid methods
An adaptive multilevel multigrid formulation for Cartesian hierarchical grid methods
复制标题
DOI：
10.1016/j.compfluid.2007.06.007
复制
发表时间：
2008-10
影响因子：
2.8
通讯作者：
D. Hartmann;M. Meinke;W. Schröder
中科院分区：
文献类型：
--
作者：
D. Hartmann;M. Meinke;W. Schröder
提出了一种自适应网格加密和多重网格加速的笛卡尔网格方法，用于求解可压缩Navier-Stokes方程。切割单元用于表示笛卡尔网格上的边界，而鬼细胞的引入，以方便实现的边界条件。单元树数据结构用于以分层方式组织网格单元。所有细化级别的单元都存在于该数据结构中，使得在多重网格上下文中需要的网格级别更改不必显式地执行。自适应网格细化介绍了使用基于现象的传感器。多层方法结合笛卡尔切割细胞的方法与弯曲边界的问题的应用进行了详细说明。带有局部时间步进的5步Runge-Kutta多重网格格式用于稳态问题，也用于非稳态问题双时间步进方法中的内积分。传统的多重网格方法的效率与嵌入边界的笛卡尔网格需要一个新的多级概念，本文介绍了这种应用程序。这个新的概念是基于以下新颖性：制定的多重网格方法的笛卡尔分层网格方法，平均控制体积的概念，和网格自适应策略，允许直接控制的数量的细化和粗化的细胞。
A Cartesian grid method with adaptive mesh refinement and multigrid acceleration is presented for the compressible Navier–Stokes equations. Cut cells are used to represent boundaries on the Cartesian grid, while ghost cells are introduced to facilitate the implementation of boundary conditions. A cell-tree data structure is used to organize the grid cells in a hierarchical manner. Cells of all refinement levels are present in this data structure such that grid level changes as they are required in a multigrid context do not have to be carried out explicitly. Adaptive mesh refinement is introduced using phenomenon-based sensors. The application of the multilevel method in conjunction with the Cartesian cut-cell method to problems with curved boundaries is described in detail. A 5-step Runge–Kutta multigrid scheme with local time stepping is used for steady problems and also for the inner integration within a dual time-stepping method for unsteady problems. The inefficiency of customary multigrid methods on Cartesian grids with embedded boundaries requires a new multilevel concept for this application, which is introduced in this paper. This new concept is based on the following novelties: a formulation of a multigrid method for Cartesian hierarchical grid methods, the concept of averaged control volumes, and a mesh adaptation strategy allowing to directly control the number of refined and coarsened cells.