Conforming and discontinuous discretizations of non-isothermal Darcy-Forchheimer flows
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908824252710912 |
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| author | Bonetti, Stefano Botti, Michele Antonietti, Paola F. |
| author_facet | Bonetti, Stefano Botti, Michele Antonietti, Paola F. |
| contents | We present and analyze in a unified setting two schemes for the numerical discretization of a Darcy-Forchheimer fluid flow model coupled with an advection-diffusion equation modeling the temperature distribution in the fluid. The first approach is based on fully discontinuous Galerkin discretization spaces. In contrast, in the second approach, the velocity is approximated in the Raviart-Thomas space, and the pressure and temperature are still piecewise discontinuous. A fixed-point linearization strategy, naturally inducing an iterative splitting solution, is proposed for treating the nonlinearities of the problem. We present a unified stability analysis and prove the convergence of the iterative algorithm under mild requirements on the problem data. A wide set of two- and three-dimensional simulations is presented to assess the error decay and demonstrate the practical performance of the proposed approaches in physically sound test cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_21630 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conforming and discontinuous discretizations of non-isothermal Darcy-Forchheimer flows Bonetti, Stefano Botti, Michele Antonietti, Paola F. Numerical Analysis 65N12, 65N30, 74F05, 76S05 We present and analyze in a unified setting two schemes for the numerical discretization of a Darcy-Forchheimer fluid flow model coupled with an advection-diffusion equation modeling the temperature distribution in the fluid. The first approach is based on fully discontinuous Galerkin discretization spaces. In contrast, in the second approach, the velocity is approximated in the Raviart-Thomas space, and the pressure and temperature are still piecewise discontinuous. A fixed-point linearization strategy, naturally inducing an iterative splitting solution, is proposed for treating the nonlinearities of the problem. We present a unified stability analysis and prove the convergence of the iterative algorithm under mild requirements on the problem data. A wide set of two- and three-dimensional simulations is presented to assess the error decay and demonstrate the practical performance of the proposed approaches in physically sound test cases. |
| title | Conforming and discontinuous discretizations of non-isothermal Darcy-Forchheimer flows |
| topic | Numerical Analysis 65N12, 65N30, 74F05, 76S05 |
| url | https://arxiv.org/abs/2508.21630 |