Resolution by Galerkin method with a special basis of a geophysical flow in open sea: a Calvi's bay simulation

Bosseur, Frédéric; Martino, Bernard Di; Orenga, Pierre

doi:10.1016/s0307-904x(99)00027-x

Cited by 7 publications

(5 citation statements)

References 14 publications

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“…The shallow water equations are based on a depth integration of an incompressible fluid conservation laws in a free surface-three dimensional domain. Governing equations for u and h can be obtained in the usual way ( [1] for example) and the two-dimensional system can be written as follows [8,7,9]:…”

Section: Mathematical Modelmentioning

confidence: 99%

Simulation of the spread of a viscous fluid using a bidimensional shallow water model

Martino¹,

Giacomoni²,

Paoli³

et al. 2011

Applied Mathematical Modelling

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In this paper we propose a numerical method to solve the Cauchy problem based on the viscous shallow water equations in an horizontally moving domain. More precisely, we are interested in a flooding and drying model, used to modelize the overflow of a river or the intrusion of a tsunami on ground. We use a non conservative form of the two-dimensional shallow water equations, in eight velocity formulation and we build a numerical approximation, based on the Arbitrary Lagrangian Eulerian formulation, in order to compute the solution in the moving domain.

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Section: Mathematical Modelmentioning

confidence: 99%

Simulation of the spread of a viscous fluid using a bidimensional shallow water model

Martino¹,

Giacomoni²,

Paoli³

et al. 2011

Applied Mathematical Modelling

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“…A basis for the PEfs has been presented in other papers (Bosseur et al, 2000) and, in this regard, only one of the main results is referred to here.…”

Section: Special Basis For the Pefsmentioning

confidence: 99%

“…Note that it is not necessary to compute this value, if only velocity and buoyancy are sought. Some experimental and numerical investigations on the marine circulation in this bay have been presented by Norro (1995) and Bosseur et al (2000).…”

Section: Time Discretizationmentioning

confidence: 99%

A Numerical Approach to Marine Circulation Using Free Surface or Rigid-lid Modeling: Application in the Bay of Calvi

Martino

Giacomoni

Orenga

2002

International Journal of Computational Fluid Dynamics

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When establishing a model of fluid flow in marine modeling, a key issue is the choice between a rigidlid approach or a free surface level model. This is not a trivial issue as it plays an important role, not only in the choice of the numerical techniques, but also in the qualitative and quantitative aspects of the numerical results. Most software use either free surface or rigid-lid hypotheses, but comparing their results is difficult, since the numerical tools used are in general, extremely different.In this work, some numerical investigations comparing rigid-lid and free surface models are presented. A numerical method using Galerkin's method, but with a new basis, is applied to solve the rigid-lid equations in a realistic domain with varying bottom. A numerical method, similar to the one already used for free surface equations (the same truncating method and precision level) is applied, where the main differences between the simulation results depend only on the model employed.In addition, a comparative simulation between rigid-lid and free surface models to study marine circulation in the bay of Calvi (Corsica) is presented, and numerical results in the non-stratified case only (fluid with constant density) are described, as no further difficulties appear in the stratified case.

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“…So, ∇u ∈ L ∞ (0, T ; W 2,r (Ω) 2 ) and as f ∈ L ∞ (0, T ; W 2,r (Ω) 2 ), we deduce from (3.56) that u ∈ L ∞ (0, T ; W 4,r (Ω) 2 ). Now, we consider (3.56) (2) and we do as previously for the bounds of the nonlinear terms. We have…”

Section: Analysis Of Some Shallow Water Problems With Rigid-lid Hypotmentioning

confidence: 99%

“…This property is interesting in a numerical viewpoint because in real cases, the depth is given in discrete form and next, this one can be smoothed with a method that implies the condition ∇H · n = 0. 2 So, we have…”

Section: Verification Of Boundary Condition Curl U =mentioning

confidence: 99%

Analysis of Some Shallow Water Problems With Rigid-Lid Hypothesis

Martino

Giacomoni

Orenga

2001

Math. Models Methods Appl. Sci.

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We present in this paper the analysis and the comparison of two two-dimensional geophysical flow problems using a rigid-lid approximation (i.e. we do not take into account the variation of surface elevation ζ). A first rigid-lid shallow water model (noted SWRL) is obtained by neglecting the variation of the surface in a weak formulation of a usual viscous shallow water model in depth-mean velocity formulation (noted SWFS for shallow water with free surface). We establish some existence results for this model and we propose a numerical resolution method. The second model we consider is an adaptation of the lake equations proposed by Levermore, Oliver and Titi, 4 in which we take into account the viscous effects, in order to compare the two approaches. For the numerical resolution, we apply the curl operator on these equations and we propose a numerical algorithm to solve this problem, that we note SWLV (shallow water for the lake with viscosity). We present finally some comparative results in an idealized configuration between the SWRL, SWLV and SWFS models (in the case where the rigid-lid approximation seems to be reasonable).

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Resolution by Galerkin method with a special basis of a geophysical flow in open sea: a Calvi's bay simulation

Cited by 7 publications

References 14 publications

Simulation of the spread of a viscous fluid using a bidimensional shallow water model

Simulation of the spread of a viscous fluid using a bidimensional shallow water model

A Numerical Approach to Marine Circulation Using Free Surface or Rigid-lid Modeling: Application in the Bay of Calvi

Analysis of Some Shallow Water Problems With Rigid-Lid Hypothesis

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