Low-Mach type approximation of the Navier-Stokes system with temperature and salinity for free surface flows
| Autor: | Boittin, Léa, Bristeau, Marie-Odile, Bouchut, François, Mangeney, Anne, Sainte-Marie, Jacques, Souillé, Fabien |
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| Přispěvatelé: | Numerical Analysis, Geophysics and Ecology (ANGE), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire Analyse et Mathématiques Appliquées (LAMA), Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS)-Université Gustave Eiffel, Centre d'Etudes et d'Expertise sur les Risques, l'Environnement, la Mobilité et l'Aménagement (Cerema), Institut de Physique du Globe de Paris, The authors acknowledge the Inria Project Lab 'Algae in Silico' for its financial support. This research is also supported by the ERC SLIDEQUAKES ERC-CG-2013-PE10-617472, Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Institut de Physique du Globe de Paris (IPG Paris) |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
AMS subject classifications. 35Q30
35Q35 76D05 76N06 Applied Mathematics General Mathematics [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation Physics::Fluid Dynamics Low-Mach approximation Free sur- face flows Layer-averaged formulation Compressible and incompressible fluids [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Variable density flows [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph] Navier-Stokes equations [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] |
| Zdroj: | Communications in Mathematical Sciences Communications in Mathematical Sciences, International Press, In press Communications in Mathematical Sciences, 2023, 21 (1), pp.151-172. ⟨10.4310/CMS.2023.v21.n1.a7⟩ |
| ISSN: | 1539-6746 1945-0796 |
| DOI: | 10.4310/CMS.2023.v21.n1.a7⟩ |
| Popis: | International audience; We are interested in free surface flows where density variations coming e.g. from temperature or salinity differences play a significant role in the hydrody-namic regime. In water, acoustic waves travel much faster than gravity and internal waves, hence the study of models arising from compressible fluid mechanics often requires a decoupling between these waves. Starting from the compressible Navier-Stokes system, we derive the so-called Navier-Stokes-Fourier system in an "incompressible" regime using the low-Mach scaling, hence filtering the acoustic waves, neglecting the density dependency on the fluid pressure but keeping its variations in terms of temperature and salinity. A slightly modified low-Mach asymptotics is proposed to obtain a model with thermo-mechanical compatibility. The case when the density depends only on the temperature is studied first. Then the variations of the fluid density with respect to temperature and salinity are considered, and it seems to be the first time that salinity dependency is considered in this low Mach limit. We give a layer-averaged formulation of the obtained models in an hydrostatic context, allowing to derive numerical schemes endowed with strong stability properties that are presented in a companion paper. Several stability properties of the layer-averaged Navier-Stokes-Fourier system are proved. |
| Databáze: | OpenAIRE |
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