A pressure-robust HHO method for the solution of the incompressible Navier-Stokes equations on general meshes
| Autor: | Daniel Castanon Quiroz, Daniele A Di Pietro |
|---|---|
| Přispěvatelé: | Université Côte d'Azur (UCA), COmplex Flows For Energy and Environment (COFFEE), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Institut Montpelliérain Alexander Grothendieck (IMAG), Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM) |
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
general meshes
65N30 Applied Mathematics General Mathematics 65N12 Numerical Analysis (math.NA) 76D05 Computational Mathematics incompressible Navier-Stokes equations pressure robustness MSC 2010: 65N08 35Q30 FOS: Mathematics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Mathematics - Numerical Analysis Hybrid High-Order methods |
| Popis: | In a recent work (Castanon Quiroz & Di Pietro (2020) A hybrid high-order method for the incompressible Navier–Stokes problem robust for large irrotational body forces. Comput. Math. Appl., 79, 2655–2677), we have introduced a pressure-robust hybrid high-order method for the numerical solution of the incompressible Navier–Stokes equations on matching simplicial meshes. Pressure-robust methods are characterized by error estimates for the velocity that are fully independent of the pressure. A crucial question was left open in that work, namely whether the proposed construction could be extended to general polytopal meshes. In this paper, we provide a positive answer to this question. Specifically, we introduce a novel divergence-preserving velocity reconstruction that hinges on the solution inside each element of a mixed problem on a subtriangulation, then use it to design discretizations of the body force and convective terms that lead to pressure robustness. An in-depth theoretical study of the properties of this velocity reconstruction, and their reverberation on the scheme, is carried out for arbitrary polynomial degrees $k\geq 0$ and meshes composed of general polytopes. The theoretical convergence estimates and the pressure robustness of the method are confirmed by an extensive panel of numerical examples. |
| Databáze: | OpenAIRE |
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