Incompressible Fluid Application

(Difference between revisions)
 Revision as of 14:21, 11 December 2009 (view source)Kazem (Talk | contribs) (→Theory)← Older edit Revision as of 14:59, 11 December 2009 (view source)Kazem (Talk | contribs) (→Theory)Newer edit → Line 41: Line 41: Computer Methods in Applied Mechanics and Engineering Computer Methods in Applied Mechanics and Engineering Vol. 191 (2002), 4295-4321'' Vol. 191 (2002), 4295-4321'' − − − This application solve the the equations.... − Mathematical approach to the problems. − − Nothing numerical − − Insert here all the references to your papers... === Numerical approach === === Numerical approach ===

General Description

Theory

The aim of this application is to solve the well known set of Navier-Stokes equations. The problem suffers from severe locking and/or instability using linear FEM.

$\partial_{t}\mathbf{u}-\nu\Delta\mathbf{u} + \mathbf{u}\cdot\nabla\mathbf{u}+\nabla p = \mathbf{f} \quad \text{in} \quad \Omega, ]0,T[$

$\quad \quad \quad \quad \quad \nabla\cdot\mathbf{u} = 0 \quad \text{in} \quad \Omega, ]0,T[$

$\mathbf{u} = \mathbf{u_{0}} \quad \text{in} \quad \Omega, t=0$

$\mathbf{u} = \mathbf{0} \qquad \text{in} \Gamma, t\in ]0,T[$

Different approaches could be chosen to solve this problem. Fractional step, Subgrid scale stabilization, GLS are among the others.

Some references to these methods are:

Stabilized finite element approximation of transient incompressible flows using orthogonal subscales Ramon Codina Computer Methods in Applied Mechanics and Engineering Vol. 191 (2002), 4295-4321

Numerical approach

All numerical details here.

This is a part quite open, depending on the application we are considering.

Every physical problem is solved defining many different ingredients. Try to be quite schematic.