Reduced-Order Modeling of Parameterized Visco-Plastic Shallow Flows
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914539836014592 |
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| author | Mizan, Md Rezwan Bin Timofeyev, Ilya Olshanskii, Maxim |
| author_facet | Mizan, Md Rezwan Bin Timofeyev, Ilya Olshanskii, Maxim |
| contents | We propose a non-intrusive reduced-order modeling framework for parametrized visco-plastic free-surface flows governed by a shallow-water formulation of Herschel--Bulkley fluids. These flows exhibit strong nonlinearities, non-smooth rheology, moving fronts, and yield surfaces, making efficient surrogate modeling particularly challenging. To address this challenge, we employ a tensor-based approach in which the solution manifold is approximated using a low-rank representation obtained via higher-order singular value decomposition of snapshot data over a structured parameter space.
The resulting tensorial reduced-order model (TROM) enables rapid online evaluation by directly reconstructing solution trajectories from the compressed representation, thereby avoiding the need to perform time integration of a reduced dynamical system. The proposed non-intrusive framework can be interpreted as an encoder--decoder architecture with a compressed latent representation and efficient multilinear decoding. Numerical experiments demonstrate that the proposed approach accurately captures key flow features, including front propagation, plug and shear regions, and near-stopping dynamics, while achieving substantial computational speedups relative to full-order simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_06526 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Reduced-Order Modeling of Parameterized Visco-Plastic Shallow Flows Mizan, Md Rezwan Bin Timofeyev, Ilya Olshanskii, Maxim Fluid Dynamics Numerical Analysis 65M22, 65F99, 76A05 We propose a non-intrusive reduced-order modeling framework for parametrized visco-plastic free-surface flows governed by a shallow-water formulation of Herschel--Bulkley fluids. These flows exhibit strong nonlinearities, non-smooth rheology, moving fronts, and yield surfaces, making efficient surrogate modeling particularly challenging. To address this challenge, we employ a tensor-based approach in which the solution manifold is approximated using a low-rank representation obtained via higher-order singular value decomposition of snapshot data over a structured parameter space. The resulting tensorial reduced-order model (TROM) enables rapid online evaluation by directly reconstructing solution trajectories from the compressed representation, thereby avoiding the need to perform time integration of a reduced dynamical system. The proposed non-intrusive framework can be interpreted as an encoder--decoder architecture with a compressed latent representation and efficient multilinear decoding. Numerical experiments demonstrate that the proposed approach accurately captures key flow features, including front propagation, plug and shear regions, and near-stopping dynamics, while achieving substantial computational speedups relative to full-order simulations. |
| title | Reduced-Order Modeling of Parameterized Visco-Plastic Shallow Flows |
| topic | Fluid Dynamics Numerical Analysis 65M22, 65F99, 76A05 |
| url | https://arxiv.org/abs/2605.06526 |