Incompressible Fluid Application
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(→Numerical approach) |
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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 == | ||
Revision as of 15:01, 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)
![\mathbf{u} = \mathbf{0} \qquad \text{in} \Gamma, t\in ]0,T[](/images/math/a/f/2/af21990dd9877e36dfb0f2ae265d88c3.png)
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 |
