FVM and FEM 1

[longnguyen25]

I ‘m analysing some CFD model by Fluent. And the algorithm in Fluent is FVM ( Finite Volume Method). I found in some fluid dynamics book that in CFD problem the FVM is better than FEM. But they didn’t speak clearly. I want to know the strong point and the weakness of FVM in comparison with FEM. In addition, can you tell me the reason why the standard k-epsilon model is used much more than the others?
Waitting for your feedbacks.Thank you very much!

 

[salmon2]

Your questions is fundamental so that I do not if I have a answer for it. I need better understanding about them.

Do not know what is FVM but I guess it is similar to finite difference method, which is for CFD. but FEA is usually for solid mechanics. Why, again I do not exactly know. But I guess one possible reason is CFD has to deal with vortex and my knowledge does not tell me FEA can handle vortex.

 

[marksummers]

My understanding is that FVM is better suited for solving CFD analysis. I recently evaluated EFD.Pro (FVM) from Flomerics and CFDesign (FEA) from Blue Ridge Numerics. Of course, they each tried to convince me that their method was best. I found a few articles that seemed to prove the FVM was better, but I am not convinced it is a big deal.

I would like to hear some more educated replies from those more familiar with the diffrences.

 

[btrueblood]

FEM for fluids historically was limited to flows without dissipation, so that the same matrix solver as used for solid mechanics could be applied. Finite difference techniques, being a time-based solution method, are more readily (understandably?) applied to time-varying problems like fluid flows, thus were the first techniques applied and have the benefit of years of development.

Around the time I was taking courses (back when we still rode our horses to the university, and the snow was 12 ft deep, uphill both ways), there were formulations for "stiffness matrices" in the finite element method that incorporated linearized Navier-stokes equations, and a few years later, newer solution techniques that would allow efficient solving of these more complex equations. A problem with the FE method is that you must specify the element type that corresponds to the flow field you are modelling (i.e. subsonic, trans-sonic or supersonic) because the equations change form from elliptical to parabolic to hyperbolic as the flow transitions thru those regimes. In a finite-difference code, the solver can be set up to determine for itself what solution method is required (but it didn't used to be that way). There are probably some nifty auto-mesh routines developed in recent years that can do the same thing for FE codes. All of this is moving towards (as in solid mechanics modelling) having the ability for users to do "push button" modelling, without any idea in their own mind of what to expect...with the usual caveats about GIGO. If that sounds like I'm advocating that you take some fluid mechanics courses before proceeding with fluid modelling, then yes, I am beating that drum, the same way solid mechanics courses will help you know when not to believe your FE stress results.

As regards k-e turbulence modelling, its use is preferred primarily because it works reasonably well, is reasonably computationally efficient (i.e. does not require modelling indivdual gas molecules), and was one of the first decent models to do so. Thus, its development progressed pretty rapidly because people used it and gained familiarity with it. Some development has been made of a k-w (kappa-omega) method that does not require as drastic a near-wall grid density, but it has its own problems too. Turbulence and boundary layer models have a long way to go before they will be truly user-friendly, much less amenable to "push button" analysis, imho. You really need to read some books, take a course, and spend a summer reading journal articles just to get reasonably familiar with them.

The biggest topic in fluid modelling lately (well, ok, 7 years ago) is that dropping costs of memory and higher processor speeds allows simulation of the "full-blown" full Reynolds-Averaged Navier-Stokes equations...but as of several years ago, the simulations had only progressed thru some limited laminar and laminar-turbulent flows; these problems were being set up and run on massively-parallel supercomputers (Beowulf clusters) and still took weeks to run...but the output was truly beautiful; you could overlay Schlieren images from the 1930's and see 1:1 correspondence from the simulations. One more step of Moore's Law, and look out, we may be able to do some of that on our desktops...or at least start seeing more rapid development of cheaper simulation methods by comparing (say) k-e models to the full RANS simulations, etc.

And, in the end, you still need to compare your results to real-world test data before anybody (including you) will trust them. Same as for FEA.

 

[pja]

Not sure what you mean by full-blown RANS..the act of averagin g the Navier-Stokes equations introduces unclosed stresses which is why you need turbulence (closure) models. So full-blown in the context of RANS always means some sort of closure approximation. Maybe what you meant was full blown Navier-Stokes equation?

 

[btrueblood]

Sorry, you're right. RANS = Reynold's-Averaged Navier Stokes, a more basic form of the Navier-Stokes, but still time-averaged, and using Reynold's stresses for closure. These are becoming more common, but again, require heavy computing resources.

I meant to say DNS, Direct Numerical Simulation of the NS equations. From wikipedia:

"Therefore, the computational cost of DNS is very high, even at low Reynolds numbers. For the Reynolds numbers encountered in most industrial applications, the computational resources required by a DNS would exceed the capacity of the most powerful computers currently available. However, direct numerical simulation is a useful tool in fundamental research in turbulence. Using DNS it is possible to perform "numerical experiments", and extract from them information difficult or impossible to obtain in the laboratory, allowing a better understanding of the physics of turbulence. Also, direct numerical simulations are useful in the development of turbulence models for practical applications, such as sub-grid scale models for Large eddy simulation (LES) and models for methods that solve the Reynolds-averaged Navier-Stokes equations (RANS). "