RUBINO , Samuele

La presente tesis aborda el modelado numérico de la turbulencia mediante modelos de Richardson y de Multiescala Variacional (VMS). En la primera parte, nos centramos en los modelos basados en el número de Richardson, que se utilizan con frecuencia en Oceanografía. El océano es un sistema básicamente turbulento. Por lo tanto, es crucial modelar...

Nous introduisons une nouvelle stratégie de modélisation de type streamline derivative basée sur projection pour la stabilisation numérique de modèles d'ordre réduit de type POD (PODROM). Comme première étape préliminaire, le modèle proposé est analysé et testé pour les équations d'advection-diffusion-réaction dominées par l'advection. Dans ce...

Nous introduisons une nouvelle strat´egie de mod´elisation de type streamline derivative bas´ee sur projection pour la stabilisation num´erique de mod`eles d'ordre r´eduit de type POD (PODROM). Comme premi`ere ´etape pr´eliminaire, le mod`ele propos´e est analys´e et test´e pour les ´equations d'advection-diffusion-r´eaction domin´ees par...

In this paper, we propose a new stabilized projection-based proper orthogonal de-composition reduced order model (POD-ROM) for the numerical simulation of incompressible flows.The new method draws inspiration from successful numerical stabilization techniques used in thecontext of finite element (FE) methods, such as local...

Proper orthogonal decomposition (POD) stabilized methods for the Navier--Stokesequations are considered and analyzed. We consider two cases: the case in which the snapshots arebased on a non inf-sup stable method and the case in which the snapshots are based on an inf-supstable method. For both cases we construct approximations to the...

In this paper, we consider up-to-date and classical Finite Element (FE) stabilized methods for timedependent incompressible flows. All studied methods belong to the Variational MultiScale (VMS) framework. So, different realizations of stabilized FE-VMS methods are compared using a high Reynolds number vortex dynamics simulation. In particular,...

In this work, we address the solution of the Navier–Stokes equations (NSE) by a Finite Element (FE) Local Projection Stabilization (LPS) method. The focus is on a LPS method that has one level, in the sense that it is defined on a single mesh, and in which the projection-stabilized structure of standard LPS methods is replaced by an...

In this paper, we propose to improve the stabilized POD-ROM introduced in [48] to deal with the numerical simulation of advection-dominated advection-diffusion-reaction equations. In particular, we propose a three-stage stabilizing strategy that will be very useful when considering very low diffusion coefficients, i.e. in the strongly...

We consider proper orthogonal decomposition (POD) methods to approximate the incompressible Navier–Stokes equations. We study the case in which one discretization for the nonlinear term is used in the snapshots (that are computed with a full order method (FOM)) and a different discretization of the nonlinear term is applied in the POD method....

The error analysis of a proper orthogonal decomposition (POD) data assimilation (DA) scheme for the Navier–Stokes equations is carried out. A grad–div stabilization term is added to the formulation of the POD method. Error bounds with constants independent on inverse powers of the viscosity parameter are derived for the POD algorithm. No upper...

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...

A finite element error analysis of a local projection stabilization (LPS) method for the time-dependent Navier–Stokes equations is presented. The focus is on the high-order term-by-term stabilization method that has one level, in the sense that it is defined on a single mesh, and in which the projection-stabilized structure of standard LPS...

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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...

Various realizations of variational multiscale (VMS) methods for simulating turbulent incompressible flows have been proposed in the past fifteen years. All of these realizations obey the basic principles of VMS methods: They are based on the variational formulation of the incompressible Navier-Stokes equations and the scale separation is...

This article presents error bounds for a velocity–pressure segregated POD reduced order model discretization of the Navier–Stokes equations. The stability is proven in L∞(L2) and energy norms for velocity, with bounds that do not depend on the viscosity, while for pressure it is proven in a semi-norm of the same asymptotic order as the L2 norm...

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 paper, we resolve several long-standing issues dealing with optimal pointwisein time error bounds for proper orthogonal decomposition (POD) reduced order modeling of the heatequation. In particular, we study the role played by difference quotients (DQs) in obtaining reducedorder model (ROM) error bounds that are optimal with ...

In this work, we study the performance of some local projection-based solvers in the Large Eddy Simulation (LES) of laminar and turbulent flows governed by the incompressible Navier–Stokes Equations (NSE). On one side, we focus on a high-order term-by-term stabilization Finite Element (FE) method that has one level, in the sense that it is...

In this paper, we propose a local projection stabilization (LPS) finite element method applied to numerically solve natural convection problems. This method replaces the projection-stabilized structure of standard LPS methods by an interpolation-stabilized structure, which only acts on the high frequencies components of the flow. This approach...