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 shawn March 3, 2004 10:43

exact solution

hi

i'm just a beginner in this cfd line as i am starting to do my research on building ventilation. i havne't got much experience on computational maths since i did pure maths for my degree. and now i'm learning from scratch.

my question might be basic and easy but i need to clarify this. say that i am using matlab to do my programming using finite element method. my question is how do i verify that the program is working.

and say i'm solving a system of pde problem (i.e: 2 laplace equations), and want to verify the program by comparing my finite element method results and the exact solution results. how can i quickly get the exact solution for the system? or do i have to solve it by hand? is there any easy way for me to refer and look for exact solutions?

 Tom March 4, 2004 05:34

Re: exact solution

In 2-dimesnions any good book on complex analysis should give a large number of exact solutions to the Laplace equation - the real and imaginary parts of any holomorphic function are harmonic.

Alternatively you can try solving the Poisson equation instead of the Laplace equation - pick a function calculate the grad^2 of it and use the result as the right hand side.

 shawn March 4, 2004 12:09

Re: exact solution-meshing the model

Thanks Tom for the guidance. I got another question which is totally different from the previous subject. It's about meshing the model. At the moment, in building my program, I'm just using a rectangular domain and just simply divide the domain into quadrilateral elements with the same width. In real life problem it is most unlikely to be the case since there's a lot of things going on in the room (at least in my case as i'm doing room ventilation) with different boundaries to be set up in line with the model.

Suppose that in the model, i've got a room with tables and computers in it. How do I start setting up the mesh for my room to include the tables and computers. If there is any good reference out there on how to start on the meshing business, pls let me know. Because every time I tried to do research on mesh generation, there's not much on the introductory side, most references are on auto mesh generation and how to create the most efficient mesh. I need s/thing much more basic.Pls help n thanks in advance.

 Jarmo Monttinen March 5, 2004 11:37

Re: exact solution-meshing the model

Perhaps this one helps: http://www.erc.msstate.edu/publications/gridbook/

Most basic CFD books have basics on grid generation as well. If you want to write your own unstructured grid generator, look up papers by Peraire and/or Löhner (late 80's, early 90s). I myself found those very useful.

-- Jarmo

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