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arXiv · 2608.07526

A Mean-Informed Low-Rank Monolithic Stochastic Galerkin Solver for the Unsteady Navier-Stokes Equations

Ahmet Kaan Aydin·Bedřich Sousedík
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Abstract

We study a low-rank solver for the stochastic unsteady incompressible Navier--Stokes equations with uncertain viscosity. The problem is discretized by a stochastic Galerkin method and written in an all-at-once (monolithic) form where the time steps are informed by a sequential solve of the mean problem. The solution vector is represented in Tensor Train (TT) format, while the system matrices are represented in CANDECOMP/PARAFAC (CP) format as needed. We propose preconditioners based on the low-rank CP approximations that retain additional stochastic and nonlinear information compared to mean-based preconditioners. Numerical experiments for a benchmark channel-flow problem are presented to show the effectiveness of the low-rank approximation, the relative tolerance strategy, and the proposed preconditioners.

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Ahmet Kaan Aydin, Bedřich Sousedík. 2026-07-18. A Mean-Informed Low-Rank Monolithic Stochastic Galerkin Solver for the Unsteady Navier-Stokes Equations. https://arxiv.org/abs/2608.07526

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