An efficient hyper reduced-order model for segregated solvers for geometrical parametrization problems
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912817461854208 |
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| author | Ngan, Valentin Nkana Stabile, Giovanni Mola, Andrea Rozza, Gianluigi |
| author_facet | Ngan, Valentin Nkana Stabile, Giovanni Mola, Andrea Rozza, Gianluigi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07082 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An efficient hyper reduced-order model for segregated solvers for geometrical parametrization problems Ngan, Valentin Nkana Stabile, Giovanni Mola, Andrea Rozza, Gianluigi Numerical Analysis 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. |
| title | An efficient hyper reduced-order model for segregated solvers for geometrical parametrization problems |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2601.07082 |