# Incompressible Fluid Application

(Difference between revisions)
 Revision as of 14:00, 11 December 2009 (view source)Kazem (Talk | contribs) (→Theory)← Older edit Revision as of 14:00, 11 December 2009 (view source)Kazem (Talk | contribs) (→Theory)Newer edit → Line 15: Line 15: [itex] − \begin{align} + &\rho\mbox{}\partial_{t}\mathbf{u}-\mu\mbox{}\Delta\mathbf{u} + \rho\mbox{}\mathbf{u}\cdot\nabla\mathbf{u}+\nabla p = \mathbf{f} \qquad \text{in} \Omega,\qquad t\in ]0,T[\\ &\rho\mbox{}\partial_{t}\mathbf{u}-\mu\mbox{}\Delta\mathbf{u} + \rho\mbox{}\mathbf{u}\cdot\nabla\mathbf{u}+\nabla p = \mathbf{f} \qquad \text{in} \Omega,\qquad t\in ]0,T[\\ &\qquad \qquad \qquad \qquad\quad \:\:\,\nabla\cdot\mathbf{\rho\mbox{}u} = 0 \qquad \text{in} \Omega,\qquad t\in ]0,T[ \\ &\qquad \qquad \qquad \qquad\quad \:\:\,\nabla\cdot\mathbf{\rho\mbox{}u} = 0 \qquad \text{in} \Omega,\qquad t\in ]0,T[ \\ &\qquad \qquad \qquad \qquad \qquad\quad\:\,\mathbf{u} = \mathbf{u_{0}} \qquad \text{in} \Omega,\qquad t=0\\ &\qquad \qquad \qquad \qquad \qquad\quad\:\,\mathbf{u} = \mathbf{u_{0}} \qquad \text{in} \Omega,\qquad t=0\\ &\qquad \qquad \qquad \qquad \qquad\quad\:\:\:\,\mathbf{u} = \mathbf{0} \qquad \text{in} \Gamma,\qquad t\in ]0,T[ &\qquad \qquad \qquad \qquad \qquad\quad\:\:\:\,\mathbf{u} = \mathbf{0} \qquad \text{in} \Gamma,\qquad t\in ]0,T[ − \end{align} + [/itex]

## 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.

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.