A Low-rank Solver for the Stochastic Unsteady Navier-Stokes Problem

06/16/2019
by   Howard C. Elman, et al.
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
03/31/2022

Krylov techniques for low-rank ADI

One of the most computationally expensive steps of the low-rank ADI meth...
research
11/04/2020

Stochastic Discontinuous Galerkin Methods with Low–Rank Solvers for Convection Diffusion Equations

We investigate numerical behaviour of a convection diffusion equation wi...
research
02/16/2023

Low-rank solutions to the stochastic Helmholtz equation

In this paper, we consider low-rank approximations for the solutions to ...
research
08/26/2019

Stochastic dynamical modeling of turbulent flows

Advanced measurement techniques and high performance computing have made...
research
06/23/2023

Computation of 2D Stokes flows via lightning and AAA rational approximation

Low Reynolds number fluid flows are governed by the Stokes equations. In...
research
08/16/2021

A fast direct solver for integral equations on locally refined boundary discretizations and its application to multiphase flow simulations

In transient simulations of particulate Stokes flow, to accurately captu...
research
06/09/2023

The effect of approximate coarsest-level solves on the convergence of multigrid V-cycle methods

The multigrid V-cycle method is a popular method for solving systems of ...

Please sign up or login with your details

Forgot password? Click here to reset