This paper presents a step forward in the formulation for incompressible fluid flow analysis using the Finite Element Method (FEM) for naval hydrodynamics problems. The necessary stabilization of convective character and incompressibility restriction are introduced via the finite increment calculus (FIC) technique. A second order implicit monolithic method, based on projection schemes, to solve Navier Stokes equations is also presented. The fluid flow equations are written in an Arbitrary Lagrangian Eulerian way, useful to treat fluid-structure interaction problems, both using the standard ALE approach or the fully Lagrangian one. Finally, some examples of application of this formulation in practical naval problems are presented.
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Il metodo degli elementi finiti (FEM) è una tecnica numerica per l’analisi e la verifica delle strutture. L’uso di tale metodo nel dimensionamento e ottimizzazione di strutture complesse è prassi consolidata da decenni in settori quali l’aerospaziale, aeronautico e automobilistico. La disponibilità odierna di hardware e software estremamente potenti a basso costo, unita alla notevolmente migliorata facilità d’uso dei suddetti codici, rende oggi possibile l’estensione del loro uso anche al di fuori dei campi di applicazione "storici". Il presente lavoro mostra sommariamente le tecniche, alcune problematiche tipiche ed i benefici dell’uso del FEM nella progettazione di strutture nautiche.
A stabilized semi-implicit fractional step algorithm based on the finite element method for solving ship wave problems using unstructured meshes is presented. The stabilized governing equations for the viscous incompressible fluid and the free surface are derived at a differential level via a finite calculus procedure. This allows us to obtain a stabilized numerical solution scheme. Some particular aspects of the problem solution, such as the mesh updating procedure and the transom stern treatment, are presented. Examples of the efficiency of the semi-implicit algorithm for the analysis of ship hydrodynamics problems are presented.
We present a general formulation for incompressible fluid flow analysis using the finite element method. The necessary stabilization for dealing with convective effects and the incompressibility condition are introduced via the Finite Calculus method using a matrix form of the stabilization parameters. This allows to model a wide range of fluid flow problems for low and high Reynolds numbers flows without introducing a turbulence model. Examples of application to the analysis of incompressible flows with moderate and large Reynolds numbers are presented.
