CFD problem using FEM, Understanding the Fluid element?

[longnguyen25]

I analysis CFD problem by using FEM.And Ansys/ Flotran is a helpful application. Now I plan to programming to solve this problem by using Matlab. But I can’t not build the system of equations [K].{q}={c} because I haven’t got all of the matrix formulas for both 2-D and 3-D fluid elements. I looked in Ansys document and many FEM FLUID BOOKS, there were only integral formulas. So can you notice me some books which I need? And it ‘ll be wonderful if you share this document with me.
Waitting for your feedbacks. Thank you very much!

 

[cbrn]

I don't understand the question. Equations of statics in order to solve for Navier-Stokes ??

 

[longnguyen25]

I 'm sorry.My question was not clearly. It is laminar incompressible flow in static case.And I want to know how to build the approximate equations to solve Navier-Stock equation. In particular I need the matrix formula of Fluid141/142-element in Ansys application.
Thank you very much!

 

[cbrn]

Hi,
as I understand it, what you are looking for should be expressed in differential form (integral formulas). However, you should look thoroughly in the Ansys Theory Reference, Chap.14 (Element Library) -> Fluid141/142. There is everything in here, but you need A LOT of patience...

Regards

 

[pja]

In FEM for fluids the strong form of the equations (differential equations) are converted to the weak form via the Galerkin method. These are the integral forms you are seeing. Then to get [K] these integrals are numerically integrated using some sort of quadrature scheme. This has to be explained in any of the books you mentioned looking at.

 

[automechanicar]

There is various literature about FEM for heat an flow problems, for example: The Finite Element Method in Heat Transfer and Fluid Dynamics, by J.N. Reddy and D.K. Gartling.

Here, you can find everything about FEM for these type of problems and of course the procedure on how to implement the equations in a code yourself, either being Matlab, Fortran or whatever. It's useful exercise as it gives a lot of insight in how FEM (for fluid flow and heat transfer) works, but you should not try to build an own code to solve more complicated problems. Afterall you have various commercial codes for this that workt fine, like Ansys.

And of course, the manual of Ansys should help you out a liitle bit too.

 

[salmon2]

Yes, totally agree with automechanicar here.

Writing your own code should be absolutely limited to really simple problem, maybe one dimension. But indeed it will help you understand the most fundamentals better than using commercial codes.

If you want to solve any problem in works, buy a commercial code which is usually supported and maintained by thousands engineer.

If you just want to have fun, you can try to write your own code, but limited to very simple problems which you can solve analytically. I still remember one time I was arrogant enough to solve a 2-d problem with Matlab in one grad course - it didn't go well, had to stalled halfway. But I still got a A though because nobody else tried 2d and they all chose to solve the 1d problem.