[andre.weiner]

Hello Foamers!

The method setReference is widely used in OpenFOAM, for instance to set a reference pressure in simulations without a boundary with fixed pressure value. It's body looks the following:

line 517-520 in fvMatrix.C
    {
        source()[celli] += diag()[celli]*value;
        diag()[celli] += diag()[celli];
    }

My Question: Why do I arrive at the defined value by manipulating the diagonal matrix coefficient and the source in the given way?

Many thanks in advance!

Best, Andre

[sharonyue]

Originally Posted by andre.weiner

Hello Foamers!

The method setReference is widely used in OpenFOAM, for instance to set a reference pressure in simulations without a boundary with fixed pressure value. It's body looks the following:

line 517-520 in fvMatrix.C
    {
        source()[celli] += diag()[celli]*value;
        diag()[celli] += diag()[celli];
    }

My Question: Why do I arrive at the defined value by manipulating the diagonal matrix coefficient and the source in the given way?

Many thanks in advance!

Best, Andre

I wrote it down and hopes this will give u some hints. pls see the image. Hopes im right


oh this image is way too big...Sorry about that, Im shocked...

[andre.weiner]

Ciao sharonyue!

Thanks a lot for your small example. I tried to formulate it a little bit more general

For each cell center P with the neighbours nb we can write the equation



or



What we want is to set for a given P



To incorporate this condition into outer algebraic system, first we multiply by



To this equation we now add (1) (we are adding 0) and get



which is reordered



This approach almost seems to simple and effective to be true
On the one hand you do not destroy the conditioning of the Matrix by applying some huge value to the diagonal and the source, and on the other hand the symmetry of the matrix is conserved (it would be also possible to set the off-diagonal coefficients to zero).

Thanks again for the support!

Best, Andre

[sharonyue]

Originally Posted by andre.weiner

Ciao sharonyue!

Thanks a lot for your small example. I tried to formulate it a little bit more general

For each cell center P with the neighbours nb we can write the equation



or



What we want is to set for a given P



To incorporate this condition into outer algebraic system, first we multiply by



To this equation we now add (1) (we are adding 0) and get



which is reordered



This approach almost seems to simple and effective to be true
On the one hand you do not destroy the conditioning of the Matrix by applying some huge value to the diagonal and the source, and on the other hand the symmetry of the matrix is conserved (it would be also possible to set the off-diagonal coefficients to zero).

Thanks again for the support!

Best, Andre

Neat! quite clear and simple,

Never too old to learn CFD. haha.

Best,
dongyue