A low-rank solver for the stochastic unsteady Navier–Stokes problem
A low-rank solver for the stochastic unsteady Navier–Stokes problem
复制标题
随机不稳定纳维斯托克斯问题的低阶求解器
DOI：
10.1016/j.cma.2020.112948
复制
发表时间：
2020
影响因子：
7.2
通讯作者：
Su, Tengfei
中科院分区：
文献类型：
--
作者：
Elman, Howard C.;Su, Tengfei
我们研究了具有随机粘度的不可压缩流的非定常纳维-斯托克斯方程的低阶迭代求解器。使用随机伽辽金方法对方程进行离散化，并且我们考虑一次性公式，其中所有时间步的代数系统都被同时收集和求解。该问题通过皮卡德方法线性化。为了在每个步骤中有效地求解线性系统，我们在 Krylov 子空间方法中使用低秩张量表示，这导致存储要求和计算成本显着降低。结合有效的基于均值的预处理器和不精确求解的思想，我们表明每个皮卡德步骤只需要少量的线性迭代。使用不同设置的二维对称步域中的流模型对所提出的算法进行了测试，以证明计算效率。
We study a low-rank iterative solver for the unsteady Navier–Stokes equations for incompressible flows with a stochastic viscosity. The equations are discretized using the stochastic Galerkin method, and we consider an all-at-once formulation where the algebraic systems at all the time steps are collected and solved simultaneously. The problem is linearized with Picard’s method. To efficiently solve the linear systems at each step, we use low-rank tensor representations within the Krylov subspace method, which leads to significant reductions in storage requirements and computational costs. Combined with effective mean-based preconditioners and the idea of inexact solve, we show that only a small number of linear iterations are needed at each Picard step. The proposed algorithm is tested with a model of flow in a two-dimensional symmetric step domain with different settings to demonstrate the computational efficiency.