Abstract
We study an iterative low-rank approximation method for the solution of the steady-state stochastic Navier-Stokes equations with uncertain viscosity. The method is based on linearization schemes using Picard and Newton iterations and stochastic finite element discretizations of the linearized problems. For computing the low-rank approximate solution, we adapt the nonlinear iterations to an inexact and low-rank variant, where the solution of the linear system at each nonlinear step is approximated by a quantity of low rank. This is achieved by using a tensor variant of the GMRES method as a solver for the linear systems. We explore the inexact low-rank nonlinear iteration with a set of benchmark problems, using a model of ow over an obstacle, under various configurations characterizing the statistical features of the uncertain viscosity, and we demonstrate its effectiveness by extensive numerical experiments.
Original language | English (US) |
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Pages (from-to) | 1275-1300 |
Number of pages | 26 |
Journal | SIAM-ASA Journal on Uncertainty Quantification |
Volume | 7 |
Issue number | 4 |
DOIs | |
State | Published - 2019 |
Externally published | Yes |
Keywords
- Low-rank approximation
- Navier-Stokes equations
- Stochastic Galerkin method
ASJC Scopus subject areas
- Statistics and Probability
- Modeling and Simulation
- Statistics, Probability and Uncertainty
- Discrete Mathematics and Combinatorics
- Applied Mathematics