# Incompressible Fluid Application

(Difference between revisions)
 Revision as of 14:20, 11 December 2009 (view source)Kazem (Talk | contribs) (→Theory)← Older edit Revision as of 14:20, 11 December 2009 (view source)Kazem (Talk | contribs) (→Theory)Newer edit → Line 30: Line 30: \mathbf{u} = \mathbf{0} \qquad \text{in} \Gamma, t\in ]0,T[ \mathbf{u} = \mathbf{0} \qquad \text{in} \Gamma, t\in ]0,T[ [/itex] [/itex] + Different approaches could be chosen to solve this problem. '''Fractional step''', '''Subgrid scale stabilization''', '''GLS''' are among the others. Different approaches could be chosen to solve this problem. '''Fractional step''', '''Subgrid scale stabilization''', '''GLS''' are among the others.

## 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

This application solve the the equations.... Mathematical approach to the problems.

Nothing numerical

Insert here all the references to your papers...

### 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.