Incompressible Fluid Application
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 |
