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A new numerical model for propagation of tsunami waves

Karel Švadlenka (2007)

Kybernetika

A new model for propagation of long waves including the coastal area is introduced. This model considers only the motion of the surface of the sea under the condition of preservation of mass and the sea floor is inserted into the model as an obstacle to the motion. Thus we obtain a constrained hyperbolic free-boundary problem which is then solved numerically by a minimizing method called the discrete Morse semi-flow. The results of the computation in 1D show the adequacy of the proposed model.

A new two-dimensional shallow water model including pressure effects and slow varying bottom topography

Stefania Ferrari, Fausto Saleri (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The motion of an incompressible fluid confined to a shallow basin with a slightly varying bottom topography is considered. Coriolis force, surface wind and pressure stresses, together with bottom and lateral friction stresses are taken into account. We introduce appropriate scalings into a three-dimensional anisotropic eddy viscosity model; after averaging on the vertical direction and considering some asymptotic assumptions, we obtain a two-dimensional model, which approximates the three-dimensional...

A new two-dimensional Shallow Water model including pressure effects and slow varying bottom topography

Stefania Ferrari, Fausto Saleri (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The motion of an incompressible fluid confined to a shallow basin with a slightly varying bottom topography is considered. Coriolis force, surface wind and pressure stresses, together with bottom and lateral friction stresses are taken into account. We introduce appropriate scalings into a three-dimensional anisotropic eddy viscosity model; after averaging on the vertical direction and considering some asymptotic assumptions, we obtain a two-dimensional model, which approximates the three-dimensional...

A novel approach to modelling of flow in fractured porous medium

Jan Šembera, Jiří Maryška, Jiřina Královcová, Otto Severýn (2007)

Kybernetika

There are many problems of groundwater flow in a disrupted rock massifs that should be modelled using numerical models. It can be done via “standard approaches” such as increase of the permeability of the porous medium to account the fracture system (or double-porosity models), or discrete stochastic fracture network models. Both of these approaches appear to have their constraints and limitations, which make them unsuitable for the large- scale long-time hydrogeological calculations. In the article,...

A null controllability data assimilation methodology applied to a large scale ocean circulation model

Galina C. García, Axel Osses, Jean Pierre Puel (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Data assimilation refers to any methodology that uses partial observational data and the dynamics of a system for estimating the model state or its parameters. We consider here a non classical approach to data assimilation based in null controllability introduced in [Puel, C. R. Math. Acad. Sci. Paris 335 (2002) 161–166] and [Puel, SIAM J. Control Optim. 48 (2009) 1089–1111] and we apply it to oceanography. More precisely, we are interested in developing this methodology to recover the unknown final...

A null controllability data assimilation methodology applied to a large scale ocean circulation model*

Galina C. García, Axel Osses, Jean Pierre Puel (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

Data assimilation refers to any methodology that uses partial observational data and the dynamics of a system for estimating the model state or its parameters. We consider here a non classical approach to data assimilation based in null controllability introduced in [Puel, C. R. Math. Acad. Sci. Paris335 (2002) 161–166] and [Puel, SIAM J. Control Optim.48 (2009) 1089–1111] and we apply it to oceanography. More precisely, we are interested in developing this methodology to recover the unknown final...

A review on the improved regularity for the primitive equations

Francisco Guillén-González, María Ángeles Rodríguez-Bellido (2005)

Banach Center Publications

In this work we will study some types of regularity properties of solutions for the geophysical model of hydrostatic Navier-Stokes equations, the so-called Primitive Equations (PE). Also, we will present some results about uniqueness and asymptotic behavior in time.

A stationary flow of fresh and salt groundwater in a heterogeneous coastal aquifer

S. Challal, A. Lyaghfouri (2000)

Bollettino dell'Unione Matematica Italiana

Si stabilisce l'esistenza e l'unicità di una soluzione monotona per il problema di frontiera libera correlato al flusso stazionare d'acqua dolce e salata intorno ad un acquifero eterogeneo. Si provano la continuità e l'esistenza di un limite asintotico della frontiera libera.

Adaptive modeling for free-surface flows

Simona Perotto (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

This work represents a first step towards the simulation of the motion of water in a complex hydrodynamic configuration, such as a channel network or a river delta, by means of a suitable “combination” of different mathematical models. In this framework a wide spectrum of space and time scales is involved due to the presence of physical phenomena of different nature. Ideally, moving from a hierarchy of hydrodynamic models, one should solve throughout the whole domain the most complex model (with...

An iterative implementation of the implicit nonlinear filter

Alexandre J. Chorin, Xuemin Tu (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Implicit sampling is a sampling scheme for particle filters, designed to move particles one-by-one so that they remain in high-probability domains. We present a new derivation of implicit sampling, as well as a new iteration method for solving the resulting algebraic equations.

An iterative implementation of the implicit nonlinear filter

Alexandre J. Chorin, Xuemin Tu (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

Implicit sampling is a sampling scheme for particle filters, designed to move particles one-by-one so that they remain in high-probability domains. We present a new derivation of implicit sampling, as well as a new iteration method for solving the resulting algebraic equations.

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