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In this paper, we introduce the evolve-then-filter (EF) regularization method for reduced order modeling of convection-dominated stochastic systems. The standard Galerkin projection reduced order model (G-ROM) yield numerical oscillations in a convection-dominated regime. The evolve-then-filter reduced order model (EF-ROM) aims at the numerical stabilization of the standard G-ROM, which uses explicit ROM spatial filter to regularize various terms in the reduced order model (ROM). Our numerical results are based on a stochastic Burgers equation with linear multiplicative noise. The numerical result shows that the EF-ROM is significantly better than G-ROM.
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Pressure Stabilization Strategies for a LES Filtering Reduced Order Model
We present a stabilized POD–Galerkin reduced order method (ROM) for a Leray model. For the implementation of the model, we combine a two-step algorithm called Evolve-Filter (EF) with a computationally efficient finite volume method. In both steps of the EF algorithm, velocity and pressure fields are approximated using different POD basis and coefficients. To achieve pressure stabilization, we consider and compare two strategies: the pressure Poisson equation and the supremizer enrichment of the velocity space. We show that the evolve and filtered velocity spaces have to be enriched with the supremizer solutions related to both evolve and filter pressure fields in order to obtain stable and accurate solutions with the supremizer enrichment method. We test our ROM approach on a 2D unsteady flow past a cylinder at Reynolds number 0≤Re≤100. We find that both stabilization strategies produce comparable errors in the reconstruction of the lift and drag coefficients, with the pressure Poisson equation method being more computationally efficient.
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- Award ID(s):
- 1953535
- PAR ID:
- 10333511
- Date Published:
- Journal Name:
- Fluids
- Volume:
- 6
- Issue:
- 9
- ISSN:
- 2311-5521
- Page Range / eLocation ID:
- 302
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/fluids6090302
