Enhanced-discretization Selective Stabilization Procedure (EDSSP)
Enhanced-discretization Selective Stabilization Procedure (EDSSP)
复制标题
增强型离散选择性稳定程序 (EDSSP)
DOI：
10.1007/s00466-006-0056-7
复制
发表时间：
2006
影响因子：
4.1
通讯作者：
S. Sathe
中科院分区：
文献类型：
--
作者：
T. Tezduyar;S. Sathe
增强离散化选择性稳定过程（EDSSP）为在不同尺度上选择性地应用数值稳定提供了一个多尺度框架。该方法基于增强离散化的多尺度函数空间概念，是增强离散化连续更新方法的基础。EDSUM是一种用于小尺度流动特性计算的多级迭代方法。它有一个内置的机制，可以在大尺度和小尺度之间传递流动信息，其方式与底层稳定配方产生的离散化一致。这是在不假设小规模试验或测试函数在增强离散区相邻大尺度元素之间的边界消失的情况下完成的。这有助于小尺度流动模式不受限制地从一个大尺度元素移动到另一个大尺度元素，而在两个元素之间的边界没有任何限制。EDSUM背后的增强离散化概念也可以方便地对不同尺度对应的方程或未知数使用不同的稳定化方法。在本文中，我们提出了一个EDSSP的版本，其中SUPG和PSPG稳定化用于对应于大尺度和小尺度的未知数，而不连续捕获稳定化用于对应于小尺度的未知数。我们还提出了一个版本，其中线性不连续捕获用于小规模未知数，非线性不连续捕获用于大规模未知数。我们用平流扩散方程控制的测试问题来评估这些版本的EDSSP的性能。
The enhanced-discretization selective stabilization procedure (EDSSP) provides a multiscale framework for applying numerical stabilization selectively at different scales. The EDSSP is based on the enhanced-discretization, multiscale function space concept underlying the enhanced- discretization successive update method (EDSUM). The EDSUM is a multi-level iteration method designed for computation of the flow behavior at small scales. It has a built-in mechanism for transferring flow information between the large and small scales in a fashion consistent with the discretizations resulting from the underlying stabilized formulations. This is accomplished without assuming that the small-scale trial or test functions vanish at the borders between the neighboring large-scale elements of the enhanced-discretization zones. This facilitates unrestricted movement of small-scale flow patterns from one large-scale element to another without any constraints at the border between the two elements. The enhanced-discretization concept underlying the EDSUM can also facilitate using different stabilizations for equations or unknowns corresponding to different scales. In this paper we propose a version of the EDSSP where the SUPG and PSPG stabilizations are used for unknowns corresponding to both the large and small scales but the discontinuity-capturing stabilizations are used for unknowns corresponding to only the small scales. We also propose a version where a linear discontinuity-capturing is used for the small-scale unknowns and a nonlinear discontinuity-capturing is used for the large-scale unknowns. We evaluate the performances of these versions of the EDSSP with test problems governed by the advection–diffusion equations.