Segregated and coupled algorithm

[cupper]

Dear All,

Generally, commercial CFD softwares use segregated algorithm that solves sequentially velocitis and pressure independently.
As far as I know, the elmer use coupled algorithm that solves velocitis and pressure in the same time.
The coupled algorithm has the advantage of getting the better accurate solution and less iteration for the convergence than segregated algorithm.
But, does the total time for convergence take longer than segregated algorithm in 3d simulation especially?
In FVM, CFX that use coupled algorithm can solve stably the flow problem of all region(incompressible, compressible).
Then, the elmer can solve the flow problem of all region stably?

Thank you,
cupper

[raback]

Hi cupper

Yes, you're right. There are different pros and cons for monolithic and segregated systems. Monolithic systems tend to consume lots of memory and this is amplified by the denser matrix topology of FE when compared to FV. Now segragated schemes split the problem into a number of simpler tasks which results to much faster computation but the scheme tends to be only conditionally stable being governed by some Courant number. Now in high Re flows there are often other reasons to keep the timestep small and hence the gains of the monolithic schemes tend to be eliminated. So I would say that if you can use a significantly larger timestep Elmer is competitive but otherwise not.

Now we are fully aware of this and there are different implementations for more robust solvers. For example, the work by Mika that you see in Ch. 32 of "Rotation form of the incompressible N-S", and also some others. So there is work beyond the standard N-S solver. These have not been utilized to the maximum and there is still room for improvements. Also the standard solver may get new vigor with the implementation of internal block precontioning strategies. The bottom line seems to be that to utilize these splitting techniques the arising linear systems have to be solved really efficiently, desirably with multigrid methods.

-Peter

[cupper]

Hi Peter,

Thank you for your reply.

There are different features between FEM(elmer, acusolve, Tdyn, etc) and FVM(OpenFOAM, fluent, CFX, etc).
Generally, FVM softwares provide advanced features such as trans-sonic/supersonic flow, cavitation, combustion, etc in addition to basic features such as incompressible, slightly compressible flow, heat transfer, turbulence, multiphase, free surface, advection of species, etc.
But, FEM softwares provide basic features mentioned above.

Is the reason a limit of FEM theory ?
or
Can i develop the advanced features from some basic features ?

Thank you,
cupper

[raback]

Hi cupper

I think that FE method does not have any inherent limitation why it is not used in more complex flow case. Though it must be said that the "basic features" are often descibed by elliptic equations while the more esoteric features require solution of parabolic and hyperbolic equations which more naturally falls under the umbrella of FV. With different upwinding and stabilzation techniques, and more advanced choice of basis functions (Discontinuous Galerkin) also the other phenomena can be dealt with.

I would also think that the situation in CFD has partially to do with the culture. FV has been the dominating method and perhaps it is more natural for engineers to code particularly for transport problems while FE has been more mathematically oriented. Also the CFD codes you refer to don't have much features in electromagnetics, solid mechanics, acoustics, quantum mechanics etc. With limited resources you have to choose your focus and then it may not be a good idea to compete with commercial codes in specialized application areas such as combustion. In fact, the models that you find in Elmer are mostly such that have been developed in some research or development project. We don't assimilate new fields just for the fun of it. But we're happy to give guidence if somebody wants to develop features for a new applications field.

-Peter