Incompressible Fluid Application

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General Description

Cylinder vel.jpg

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[


\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

Theory

Using the Application

Examples

Programming Documentation

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