[tomd97]

Hi,
I'm just trying to understand the theory behind how CFX discretises the Navier Stokes equations. I'm writing a thesis on external aerodynamics study. In the link below from ANSYS it says that a hybrid combination of the finite volume method and finite element method is used to discretise the Navier Stokes equation.

http://www.anflux.com/design/default...04c276a82c1ade

The finite volume method I assume is is simply a case of applying flux in = flux out at each control volume. Not sure how the Navier Stokes equations comes into this but I'll take it as that for now.

Waht I dont understand is how the finite element method is used. I've taken an FEA class at college and the general method seems to be to generate a matrix of equations from variables at the nodes (We've only done this for solid structures) so equations will be in the form [F]=[k][u] .

So I'm assuming ANSYS uses the finite element method by doing something like this:
[delta P] = [R][v]
where delta P is pressure gradient between two nodes, R is the resistance to flow (between two nodes?) and v is the velocity vector to at all points. Would this be something like how ANSYS appraoches this. Also I'd understand how resistance to flow might be calculated in a pipe (hagen-pouseille law maybe?), but not in terms of external aerodynamics. I only need a general understanding of how the code operates, so any guidance at all would be appreciated.
Also how does the code act like a "hybrid"? does it simply conduct both the finite element method and finite volume method and compare results?
Thanks
Regards
Tom

[AtoHM]

Hi, I am a student as well and here are some hints or things I got out of literature I found. If I am wrong, pls correct.

The finite volume approach is used for CFD, because unlike finite element approach it is better at capturing for example shocks within the flow. Shocks are instantly changing relevant values like pressure, temperature, entropy, so they should be well-covered. Solid structures dont inherit such jumps, which is the reason FE is used there.

The NSE are conservation of mass, momentum and energy (not only mass as you wrote). So for each element the mass equilibrium, as well as momentum (in 3 directions) and energy are calculated, which gives 5 equations. Discretization means, that each value comes from a Taylor-Series at each node, where only a few parts of the total series are considered. Depending how many parts you take, the error is smaller, but this can also lead to other disadvantages. The resulting system also has the form Ax = b, where A is a huge matrix, x contains the wanted variables and b is another vector. This is solved by inverting A iteratively by Incomplete-Lower-Upper Decomposition.

[Antanas]

Very sketchy description. FV methodology is in that you take your PDEs and integrate 'em over each control volume, then using Gauss’ Divergence Theorem you convert volume integrals involving divergence and gradient operators to surface integrals, then you discretize the volume and surface integrals to get algebraic equations.

As for FEM in CFX, solution fields and other properties are stored at the mesh nodes. To evaluate many of the terms, the solution field or solution gradients must be approximated at integration points. ANSYS CFX uses finite-element shape functions to perform these approximations.

All that info you may find in CFX Theory Guide, Section 11.1.1. So, RTFM.