A low-rank solver for the stochastic unsteady Navier–Stokes problem

Elman, Howard C.; Su, Tengfei

doi:10.1016/j.cma.2020.112948

A low-rank solver for the stochastic unsteady Navier–Stokes problem

Journal Article · Thu Mar 05 23:00:00 EST 2020 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2020.112948· OSTI ID:1801900

Elman, Howard C. ^[1]; ^[2]

University of Maryland, College Park, MD (United States); OSTI
University of Maryland, College Park, MD (United States)

Here 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.

View Accepted Manuscript (DOE)

Research Organization:: University of Maryland, College Park, MD (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); National Science Foundation (NSF)

Grant/Contract Number:: SC0009301

OSTI ID:: 1801900

Alternate ID(s):: OSTI ID: 1603384

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Journal Issue: C Vol. 364; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
all-at-once system
low-rank tensor approximation
stochastic Galerkin method
time-dependent Navier–Stokes

A low-rank solver for the stochastic unsteady Navier–Stokes problem

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