Incompressible Fluid Application
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| − | \quad \quad \quad \quad \quad \nabla\cdot\mathbf{u} = 0 | + | \quad \quad \quad \quad \quad \nabla\cdot\mathbf{u} = 0 \quad \text{in} \quad \Omega, ]0,T[ |
</math> | </math> | ||
| + | <math> | ||
| + | \mathbf{u} = \mathbf{u_{0}} \quad \text{in} \quad \Omega, t=0 | ||
| + | </math> | ||
This application solve the the equations.... | This application solve the the equations.... | ||
Revision as of 14:11, 11 December 2009
Contents |
General Description
ADVERTISMENT STYLE no numerical details!!! |
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[](/images/math/d/0/b/d0b6d9ab6388ed55bb44b341fe0f5c6e.png)
![\quad \quad \quad \quad \quad \nabla\cdot\mathbf{u} = 0 \quad \text{in} \quad \Omega, ]0,T[](/images/math/4/c/8/4c8241443bc9a98e420f12b6b70063d5.png)
This application solve the the equations.... Mathematical approach to the problems.
Nothing numerical
Insert here all the references to your papers...
\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{0} \qquad \text{in} \Gamma,\qquad t\in ]0,T[
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.
