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An evolve-filter-relax stabilized reduced order stochastic collocation method for the time-dependent Navier-Stokes equations. (English) Zbl 1428.65029

Summary: In this paper, we propose a filter-based stabilization of reduced order models (ROMs) for uncertainty quantification (UQ) of the time-dependent Navier-Stokes equations in convection-dominated regimes. We propose a novel high-order ROM differential filter and use it in conjunction with an evolve-filter-relax (EFR) algorithm to attenuate the numerical oscillations of standard ROMs. We also examine how stochastic collocation methods can be combined with the EFR algorithm for efficient UQ of fluid flows. We test the new framework in the numerical simulation of a two-dimensional flow past a circular cylinder with a random viscosity that yields a random Reynolds number with mean \(\mathrm{Re}=100\).

MSC:

65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
35Q30 Navier-Stokes equations
65C30 Numerical solutions to stochastic differential and integral equations

Software:

redbKIT; pyMOR; Tasmanian
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Full Text: DOI

References:

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