dorsal/arxiv
View SchemaAn efficient hyper reduced-order model for segregated solvers for geometrical parametrization problems
| Authors | Valentin Nkana Ngan, Giovanni Stabile, Andrea Mola, Gianluigi Rozza |
|---|---|
| Categories | |
| ArXiv ID | 2601.07082vv1 |
| URL | https://arxiv.org/abs/2601.07082 |
| License | http://creativecommons.org/licenses/by/4.0/ |
Abstract
We propose an efficient hyper-reduced order model (HROM) designed for segregated finite-volume solvers in geometrically parametrized problems. The method follows a discretize-then-project strategy: the full-order operators are first assembled using finite volume or finite element discretizations and then projected onto low-dimensional spaces using a small set of spatial sampling points, selected through hyper-reduction techniques such as DEIM. This approach removes the dependence of the online computational cost on the full mesh size. The method is assessed on three benchmark problems: a linear transport equation, a nonlinear Burgers equation, and the incompressible Navier--Stokes equations. The results show that the hyper-reduced models closely match full-order solutions while achieving substantial reductions in computational time. Since only a sparse subset of mesh cells is evaluated during the online phase, the method is naturally parallelizable and scalable to very large meshes. These findings demonstrate that hyper-reduction can be effectively combined with segregated solvers and geometric parametrization to enable fast and accurate CFD simulations.
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"abstract": "We propose an efficient hyper-reduced order model (HROM) designed for segregated finite-volume solvers in geometrically parametrized problems. The method follows a discretize-then-project strategy: the full-order operators are first assembled using finite volume or finite element discretizations and then projected onto low-dimensional spaces using a small set of spatial sampling points, selected through hyper-reduction techniques such as DEIM. This approach removes the dependence of the online computational cost on the full mesh size. The method is assessed on three benchmark problems: a linear transport equation, a nonlinear Burgers equation, and the incompressible Navier--Stokes equations. The results show that the hyper-reduced models closely match full-order solutions while achieving substantial reductions in computational time. Since only a sparse subset of mesh cells is evaluated during the online phase, the method is naturally parallelizable and scalable to very large meshes. These findings demonstrate that hyper-reduction can be effectively combined with segregated solvers and geometric parametrization to enable fast and accurate CFD simulations.",
"arxiv_id": "2601.07082",
"authors": [
"Valentin Nkana Ngan",
"Giovanni Stabile",
"Andrea Mola",
"Gianluigi Rozza"
],
"categories": [
"math.NA",
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],
"license": "http://creativecommons.org/licenses/by/4.0/",
"title": "An efficient hyper reduced-order model for segregated solvers for geometrical parametrization problems",
"url": "https://arxiv.org/abs/2601.07082",
"version": "v1"
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