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-   -   Implementation of Robin BC by groovyBC : difference wrt. theoretic solution (http://www.cfd-online.com/Forums/openfoam-programming-development/99669-implementation-robin-bc-groovybc-difference-wrt-theoretic-solution.html)

tianyikillua April 9, 2012 12:24

Implementation of Robin BC by groovyBC : difference wrt. theoretic solution
 
1 Attachment(s)
Hello everyone, we consider the following stationary heat equation:

Laplacian(T)=0

Code:

-----------T(x)---------- a bar with length L=0.4 m, mesh Delta x=1 mm
x=0        x          x=L (patch outlet)

BC :
At x=0 : T(0)=T0=273 K
At x=L : kT'(x)=h*(T(L)-Tinf) with k=237 W/mK, h=-100 W/m^2K, Tinf=873 K

We have implemented this BC using swak4Foam, in 0/T for the patch outlet:
Code:

            type                groovyBC;
            variables          "k=237;h=-100;Tinf=873;";
            valueExpression    "Tinf";
            fractionExpression  "1/(1-k/(mag(delta())*h))";
            value                    $internalField;

We are using the "steadylaplacianFoam" where we solve only the stationary heat equation. After about 5 iterations the solution OF has converged.

However, the OF solution differs a little from the theoretic solution :

Attachment 12409

gschaider April 11, 2012 17:20

Quote:

Originally Posted by tianyikillua (Post 353794)
Hello everyone, we consider the following stationary heat equation:

Laplacian(T)=0

Code:

-----------T(x)---------- a bar with length L=0.4 m, mesh Delta x=1 mm
x=0        x          x=L (patch outlet)

BC :
At x=0 : T(0)=T0=273 K
At x=L : kT'(x)=h*(T(L)-Tinf) with k=237 W/mK, h=-100 W/m^2K, Tinf=873 K

We have implemented this BC using swak4Foam, in 0/T for the patch outlet:
Code:

            type                groovyBC;
            variables          "k=237;h=-100;Tinf=873;";
            valueExpression    "Tinf";
            fractionExpression  "1/(1-k/(mag(delta())*h))";
            value                    $internalField;

We are using the "steadylaplacianFoam" where we solve only the stationary heat equation. After about 5 iterations the solution OF has converged.

However, the OF solution differs a little from the theoretic solution :

Attachment 12409

Convergence is relative. Have you tried a stricter convergence criterion? Also try varying the mesh resolution to see if this is not just a discretization problem

tianyikillua April 12, 2012 11:33

After we changed the gradient scheme to leastSquares, everything is fine !! However we still don't know why...


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