[brent_craven]

Hi All,

I am currently running a simple heat conduction problem on a plate, where one side is given a uniform heat flux via the "fixedGradient" BC and all other sides are insulated. So, theoretically the plate should *uniformly* heat up over time.

The test case that I put together to illustrate the problem includes a non-uniform structured mesh, where the wall spacing next to the fixedGradient patch varies as shown below:

mesh.jpg

If I use "laplacianFoam" to solve for transient conduction in the plate, because the near-wall mesh spacing is non-uniform, I get a highly non-uniform temperature distribution along the fixedGradient patch and in the plate, which is non-physical - as shown below:

Tcontours.jpg

As you can see. There is a problem, especially since this non-uniform temperature distribution leads to a non-physical heat flux in the other directions.

Looking at the source code for the "fixedGradient" BC, in the "evaluate" member function, the cause of this is obvious. As shown below, this first-order implementation leads to boundary patch values that depend on the near-wall spacing.

    
Field<Type>::operator=
    (
        this->patchInternalField() + gradient_/this->patch().deltaCoeffs()
    );

So, my questions are:
1. Is this just to be expected given the first order nature of the boundary condition? I.e., is this just a result of non-uniform discretization error?

2. If I require a heat flux BC on a mesh that has non-uniform near-wall spacing (e.g., a very complex unstructured mesh), how can this be accomplished? Is there another approach to implementing a fixedGradient/heat flux boundary condition that will be much less dependent on the near-wall mesh spacing?


If you are interested, here is a link to this test case that can be run with "laplacianFoam":

http://dl.dropbox.com/u/2969338/fixe...ntTestCase.tgz


Thanks for your input. I appreciate any thoughts people have.

Thanks!

Brent