GÓMEZ MÁRMOL , María Macarena

En este trabajo se hace un estudio, desde el punto de vista teórico de algunos problemas que aparecen en la Mecánica de Fluidos que corresponden a sistemas de Ecuaciones en Derivadas Parciales no Lineales. En concreto, se estudian dos modelos de turbulencia con una y dos ecuaciones respectivamente. Esta Memoria se divide en tres principales:...

Nous étudions un système non-linéaire d'équations du type parabolique provenant de la modélisation de la turbulence. Les inconnues sont les N composantes du champ des vitesses u couplées avec deux grandeurs scalaires θ et ϕ. Ce système présente un terme de diffusion non-linéaire sous forme matricielle A(θ,ϕ) et les termes sources non-linéaires...

We introduce in this paper some elements for the mathematical analysis of turbulence models for oceanic surface mixing layers. We consider Richardson-number based vertical eddy diffusion models. We prove the existence of unsteady solutions if the initial condition is close to an equilibrium, via the inverse function theorem in Banach spaces. We...

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We propose a finite element discretization of the Navier–Stokes equations that relies on the variational multi-scale approach together with the addition of a Smagorinsky type viscosity, in order to take into account possible subgrid turbulence. We recall that the discrete problem admits a solution and prove a priori error estimates. Next we...

In this paper we investigate the finite-time and asymptotic behaviour of algebraic turbulent mixing-layer models by numerical simulation. We compare the performances given by three different settings of the eddy viscosity. We consider Richardson number-based vertical eddy viscosity models. Two of these are classical algebraic turbulence models...

In this paper, we study the stability of oceanic turbulent mixing layers by the finite element method with respect to perturbations of the data. We prove that the equilibria states depend continuously on the data, and that they are asymptotically stable in time, when approximated by standard numerical schemes. We also perform some numerical...

This paper deals with the numerical analysis of a finite element projection-based VMS turbulence model that includes general non-linear wall laws. Only a single mesh and interpolation operators on a virtual coarser mesh are needed to implement the model. We include a projection-stabilization of pressure to use the same interpolation for...

In this work, we introduce an iterative optimization algorithm to obtain the intrinsic Proper Generalized Decomposition modes of elliptic partial differential equations. The main idea behind this procedure is to adapt the general Gradient Descent algorithm to the algebraic version of the intrinsic Proper Generalized Decomposition framework, and...

En este trabajo realizamos un an alisis de paso al l mite singular en una ecuaci ón evolutiva de convecci ón-difusióon, imponiendo el flujo total normal en la frontera de entrada de flujo y una condici on de tipo Newmann en el resto de la frontera. Probamos que la soluci ón de este problema converge en L2 (Q) a la de la ecuaci ón de convecci...

We introduce a low-order stabilized discretization of the Primitive Equations of the Ocean, with a highly reduced computational complexity. We prove stability through a specific inf-sup condition, and weak convergence to a weak solution. We also perform some numerical test for relevant flows.

We present a reduced basis Smagorinsky model. This model includes a non-linear eddy diffusion term that we have to treat in order to solve efficiently our reduced basis model. We approximate this non-linear term using the Empirical Interpolation Method, in order to obtain a linearised decomposition of the reduced basis Smagorinsky model. The...

En este trabajo estudiamos la resolución de las Ecuaciones de Navier-Stokes estacionarias mediante métodos distributivos no lineales. Formulamos estos métodos como métodos de tipo Petrov-Galerkin, en un contexto de discretización por el método de los elementos finitos. Utilizamos funciones tests descentradas "corriente arriba"para el...