[swak4Foam] Implementation of Robin BC by groovyBC : difference wrt. theoretic solution

tianyikillua · April 9, 2012, 11:24

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 :

CL.jpg

gschaider · April 11, 2012, 16:20

Quote:

Originally Posted by tianyikillua

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, 10:33

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

April 9, 2012, 11:24	Implementation of Robin BC by groovyBC : difference wrt. theoretic solution	#1
tianyikillua New Member Tianyi LI Join Date: Mar 2012 Posts: 4 Rep Power: 14	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 : CL.jpg

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April 12, 2012, 10:33		#3
tianyikillua New Member Tianyi LI Join Date: Mar 2012 Posts: 4 Rep Power: 14	After we changed the gradient scheme to leastSquares, everything is fine !! However we still don't know why...