# Incompressible Fluid Application

(Difference between revisions)
 Revision as of 14:59, 11 December 2009 (view source)Kazem (Talk | contribs) (→Theory)← Older edit Revision as of 15:01, 11 December 2009 (view source)Kazem (Talk | contribs) (→Numerical approach)Newer edit → Line 50: Line 50: Every physical problem is solved defining many different ingredients. Every physical problem is solved defining many different ingredients. Try to be quite schematic. Try to be quite schematic. + ==== elements ==== + {| class="wikitable" width="100%" style="text-align:left; background:#d0d9dd; border:0px solid #e1eaee; font-size:100%; -moz-border-radius-topleft:0px; -moz-border-radius-bottomleft:0px; padding:0px 0px 0px 0px;" valign="top" + !Element + !Type + !Geometry + !Nonlinearity + !Material Type + |-style="background:#F1FAFF;" + | [[TotalLagrangian]] + | Solid + | 2D,3D Geometries + | Large Displacement + | Isotropic + |-style="background:#F1FAFF;" + | [[ShellIsotropic]] + | Shell + | 3D Triangle + | Large Displacement + | Isotropic + |-style="background:#F1FAFF;" + | [[ShellAnisotropic]] + | Shell + | 3D Triangle + | Large Displacement + | Orthotropic + |-style="background:#F1FAFF;" + | [[CrisfieldTrussElement]] + | Truss + | Line + | Large Displacement + | Isotropic + |-style="background:#F1FAFF;" + | [[KinematicLinear]] + | + | + | + | + |} == Theory == == Theory ==

## 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.

#### elements

Element Type Geometry Nonlinearity Material Type
TotalLagrangian Solid 2D,3D Geometries Large Displacement Isotropic
ShellIsotropic Shell 3D Triangle Large Displacement Isotropic
ShellAnisotropic Shell 3D Triangle Large Displacement Orthotropic
CrisfieldTrussElement Truss Line Large Displacement Isotropic
KinematicLinear