Some Mathematical Aspects of Geophysical Fluid Dynamic Equations

Témam, Roger

doi:10.1007/s00032-003-0019-9

Cited by 14 publications

(4 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The equations of geophysical fluid dynamics governing the motion of the ocean and the atmosphere are derived from the conservation laws from physics. In the case of a largescale ocean (see, e.g., [10,22,23,26,27,28]), it is considered as made up of a slightly compressible fluid modelled by conservation of momentum and mass equations, with variable density (depending on temperature and salinity) and Coriolis acceleration.…”

Section: Classical Hydrostatic Stokes Formulations In Oceanographymentioning

confidence: 99%

Stabilized Schemes for the Hydrostatic Stokes Equations

Guillén-González¹,

Galván²

2015

SIAM J. Numer. Anal.

View full text Add to dashboard Cite

Some new stable finite element (FE) schemes are presented for the hydrostatic Stokes system or primitive equations of the ocean. It is known that the stability of the mixed formulation approximation for primitive equations requires the well-known Ladyzhenskaya-Babuška-Brezzi condition related to the Stokes problem and an extra inf-sup condition relating the pressure and the vertical velocity [F. Guillén-González and J. R. Rodríguez-Galván, Numer. Math., 130 (2015), pp. 225-256]. The main goal of this paper is to avoid this extra condition by adding a residual stabilizing term to the vertical momentum equation. Then, the stability for Stokes-stable FE combinations is extended to the primitive equations and some error estimates are provided using Taylor-Hood P 2 -P 1 or minielement (P 1 +bubble)-P 1 FE approximations, showing the optimal convergence rate in the P 2 -P 1 case. These results are also extended to the anisotropic (nonhydrostatic) problem. On the other hand, by adding another residual term to the continuity equation, a better approximation of the vertical derivative of pressure is obtained. In this case, stability and error estimates including this better approximation are deduced, where optimal convergence rate is deduced in the (P 1 +bubble)-P 1 case. Finally, some numerical experiments are presented supporting previous results.

show abstract

Section: Classical Hydrostatic Stokes Formulations In Oceanographymentioning

confidence: 99%

Stabilized Schemes for the Hydrostatic Stokes Equations

Guillén-González¹,

Galván²

2015

SIAM J. Numer. Anal.

View full text Add to dashboard Cite

show abstract

“…Also, an asymptotic analysis and the finite‐dimensional behavior of the 3D viscous PEs in a thin domain as the depth of the domain goes to zero were studied in and . For a more extensive discussion and review on this subject, the reader is referred to the recent articles and .…”

Section: Introductionmentioning

confidence: 99%

A second-order decoupled implicit/explicit method of the 3D primitive equations of ocean II: finite element spatial discretization

Chen

2016

Int. J. Numer. Meth. Engng

View full text Add to dashboard Cite

SUMMARYA fully discrete second-order decoupled implicit/explicit method is proposed for solving 3D primitive equations of ocean in the case of Dirichlet boundary conditions on the side, where a second-order decoupled implicit/explicit scheme is used for time discretization, and a finite element method based on the P 1 .P 1 / P 1 P 1 .P 1 / elements for velocity, pressure and density is used for spatial discretization of these primitive equations. Optimal H KEY WORDS: primitive equations of ocean; optimal error estimates; P 1 .P 1 / P 1 P 1 .P 1 / finite element spaces; second-order decoupled implicit/explicit method

show abstract

“…Given a smooth bounded domain M ⊂ R 2 and the cylindrical domain 0 = M × (−h, 0) ⊂ R 3 , consider in 0 the following well known system of 3D viscous Primitive Equations (PEs) of Geophysical Fluid Dynamics (see e.g. [8], [26]- [28], [31,32], [39,40] and the references therein). Conservation of horizontal momentum:…”

mentioning

confidence: 99%

“…Existence and uniqueness of strong solutions, global in time, to the viscous 3D PEs in thin domains for a large set of initial data whose sizes depend inversely on the thickness of the domain were established in [17]. For a more extensive discussion and review on this subject, we refer the reader to the recent articles [39] and [40].…”

mentioning

confidence: 99%

The global attractor for the solutions to the 3D viscous primitive equations

Ju¹

2007

Discrete &Amp; Continuous Dynamical Systems - A

113

140

View full text Add to dashboard Cite

Existence of the global attractor is proved for the strong solutions to the 3D viscous Primitive Equations (PEs) modeling large scale ocean and atmosphere dynamics. This result is obtained under the natural assumption that the external heat source Q is square integrable. Furthermore, it is shown in [20] that the fractal and Hausdroff dimensions of the global attractor for 3D viscous PEs are both finite.

show abstract

Some Mathematical Aspects of Geophysical Fluid Dynamic Equations

Cited by 14 publications

References 14 publications

Stabilized Schemes for the Hydrostatic Stokes Equations

Stabilized Schemes for the Hydrostatic Stokes Equations

A second-order decoupled implicit/explicit method of the 3D primitive equations of ocean II: finite element spatial discretization

The global attractor for the solutions to the 3D viscous primitive equations

Contact Info

Product

Resources

About