Academic Journal
Analysis of dissipation operators that damp spurious modes while maintaining discrete approximate geostrophic equilibriums for the B-grid staggered scheme on triangular meshes
| العنوان: | Analysis of dissipation operators that damp spurious modes while maintaining discrete approximate geostrophic equilibriums for the B-grid staggered scheme on triangular meshes |
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| المؤلفون: | Do, Minh-Hieu, Nguyen, Van-Thanh, Omnes, Pascal |
| المساهمون: | CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Université Paris Dauphine-PSL, Université Paris Sciences et Lettres (PSL)-Université Paris Sciences et Lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Algorithms and parallel tools for integrated numerical simulations (ALPINES), Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques (INSMI-CNRS)-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 Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Service de Génie Logiciel pour la Simulation (SGLS), Département de Modélisation des Systèmes et Structures (DM2S), Institut des Sciences Appliquées et de la Simulation pour les énergies bas carbone (ISAS), CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire) (CEA-DES (ex-DEN)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire) (CEA-DES (ex-DEN)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Institut des Sciences Appliquées et de la Simulation pour les énergies bas carbone (ISAS), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay |
| المصدر: | ISSN: 0021-9991. |
| بيانات النشر: | HAL CCSD Elsevier |
| سنة النشر: | 2023 |
| مصطلحات موضوعية: | Low Froude number, Hodge decomposition, Staggered schemes, Spurious mode damping, geostrophic equilibrium, Shallow water equation with Coriolis source term, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], [MATH]Mathematics [math], [PHYS]Physics [physics] |
| الوصف: | International audience ; We consider the lowest order - so called B-grid - discretization on triangular cells which is common in the ocean or atmosphere simulation science, with pressure field at the vertices of the triangles and the velocity field at the cell centers. It is known that this discretization presents spurious modes due to a too large number of velocities unknowns and that these modes should be damped; since preservation of approximate geostrophic equilibrium (GE) may be of primary importance in the simulations, we propose and analyze damping operators that, when applied to the linearized constant coefficient configuration, exactly preserve discrete versions of the GEs. We also analyze their effects in more general configurations and their possible coupling with more standard damping operators. These strategies cover triangular variants of the Low Froude (LF) scheme [1], the Apparent Topography (AT) scheme [2, 3], as well as a new modification of it. The LF scheme has no numerical diffusion terms in the pressure equation and damps the normal velocity jumps between adjacent cells in the momentum equation. In the AT scheme, numerical diffusion is added in the pressure equation in such a way that it does not impact the discrete GE. However, since the AT scheme alone cannot be proved to be damping through energy estimates and does not preserve the space which is orthogonal to the discrete GE, we also study what we call the Modified Apparent Topography (MAT) that satisfies these important properties. We also suggest semi-implicit time discretizations that preserve these properties. Extensions to the full non-linear equations are also provided. Numerical experiments illustrate the performance of the new schemes. |
| نوع الوثيقة: | article in journal/newspaper |
| اللغة: | English |
| DOI: | 10.1016/j.jcp.2023.112261 |
| الاتاحة: | https://hal.science/hal-03834155 https://hal.science/hal-03834155v2/document https://hal.science/hal-03834155v2/file/Final_elsarticle_Analysis_of_staggered_schemes.pdf https://doi.org/10.1016/j.jcp.2023.112261 |
| Rights: | info:eu-repo/semantics/OpenAccess |
| رقم الانضمام: | edsbas.50982F67 |
| قاعدة البيانات: | BASE |
| DOI: | 10.1016/j.jcp.2023.112261 |
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