Solving heat equation

Reptider · May 19, 2021, 17:16

Hello!
I have some mesh created by cartesianMesh (Surface.jpg). All cells and boundary faces are filled by constant aT field. I want to heat it using this heat equation:

Code:

while (simple.correctNonOrthogonal())
{
     fvScalarMatrix TEqn
     (
          fvm::ddt(T) - fvm::laplacian(aT, T)
     );
     TEqn.solve();
}

There is fixedGradient as boundary condition.
But I get strangth results. There are 3 time steps: 0.001, 0.002 and 0.003 (TField_0.001.jpg, TField_0.002.jpg and TField_0.003.jpg respectively). We can see waves at the boundary that dissapear with increasing time step.
Why do they appear at first steps? Is heat equation solved right?
By the way, mesh has idential waves.
Surface.jpg
TField_0.001.jpg
TField_0.002.jpg
TField_0.003.jpg

Tobermory · May 21, 2021, 12:39

Probably a result of your mesh - it's not very clean - there are large jumps in mesh size between adjacent cells. This probably causes the perturbation ... but the perturbation is tiny - a few hundedth's of a Kelvin ... why are you worried?

If you need to get rid of the waviness, I'd suggest using a different meshing approach to improve your solution.

May 19, 2021, 17:16	Solving heat equation	#1
Reptider New Member Join Date: Sep 2020 Posts: 28 Rep Power: 5	Hello! I have some mesh created by cartesianMesh (Surface.jpg). All cells and boundary faces are filled by constant aT field. I want to heat it using this heat equation: Code: while (simple.correctNonOrthogonal()) { fvScalarMatrix TEqn ( fvm::ddt(T) - fvm::laplacian(aT, T) ); TEqn.solve(); } There is fixedGradient as boundary condition. But I get strangth results. There are 3 time steps: 0.001, 0.002 and 0.003 (TField_0.001.jpg, TField_0.002.jpg and TField_0.003.jpg respectively). We can see waves at the boundary that dissapear with increasing time step. Why do they appear at first steps? Is heat equation solved right? By the way, mesh has idential waves. Surface.jpg TField_0.001.jpg TField_0.002.jpg TField_0.003.jpg

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May 21, 2021, 12:39		#2
Tobermory Senior Member Join Date: Apr 2020 Location: UK Posts: 668 Rep Power: 14	Probably a result of your mesh - it's not very clean - there are large jumps in mesh size between adjacent cells. This probably causes the perturbation ... but the perturbation is tiny - a few hundedth's of a Kelvin ... why are you worried? If you need to get rid of the waviness, I'd suggest using a different meshing approach to improve your solution.