Preconditioning Steady-State Navier--Stokes Equations with Random Data
Preconditioning Steady-State Navier--Stokes Equations with Random Data
复制标题
随机数据预处理稳态纳维-斯托克斯方程
DOI：
10.1137/120870578
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发表时间：
2012
影响因子：
3.1
通讯作者：
Powell C
中科院分区：
文献类型：
--
作者：
Powell C
本文研究了具有不确定数据的定常Navier-Stokes方程的数值解。具体来说，我们处理的情况下，不确定的粘度，这导致在一个不确定的雷诺数的流动。线性化后，我们应用随机Galerkin有限元方法，结合标准的inf-sup稳定的Taylor-Hood近似的空间域（高度拉伸网格）与正交多项式的随机参数。这就产生了一系列具有Kronecker乘积结构的非对称鞍点问题。本研究的新贡献在于这些离散系统的高效块三角预条件器的建设，用于GMRES。至关重要的是，预条件是强大的离散化和统计参数，我们利用现有的确定性求解器的基础上，所谓的压力对流扩散和最小二乘整流子近似。
We consider the numerical solution of the steady-state Navier--Stokes equations with uncertain data. Specifically, we treat the case of uncertain viscosity, which results in a flow with an uncertain Reynolds number. After linearization, we apply a stochastic Galerkin finite element method, combining standard inf-sup stable Taylor--Hood approximation on the spatial domain (on highly stretched grids) with orthogonal polynomials in the stochastic parameter. This yields a sequence of nonsymmetric saddle-point problems with Kronecker product structure. The novel contribution of this study lies in the construction of efficient block triangular preconditioners for these discrete systems, for use with GMRES. Crucially, the preconditioners are robust with respect to the discretization and statistical parameters, and we exploit existing deterministic solvers based on the so-called pressure convection-diffusion and least-squares commutator approximations.