solve the equation looks like heat conduction equation

ythw · October 27, 2023, 08:58

Hello,

I want to use OenFOAM to solve a partial differential equation,which looks like heat conduction equation. But its "thermal diffusion coefficient" is less than 0.

It is
fvm::ddt(T) - fvm::laplacian(DT, T)
==
0
But its Dt < 0.

I tried to use laplacianFoam, but the calculation failed. "Floating point exception" appears. Can someone tell me how to adjust my laplacianFoam case, or which solver I should choose?

Tobermory · October 27, 2023, 12:18

Is the equation not unstable with a negative diffusion coefficient, i.e. working as intended?

Think of a simple case of 1D heat conduction in a bar with a negative heat diffusivity - any gradient would automatically try steepen instead of diffuse. So I can imagine that your solution would run away quickly, and ultimately crash.

October 27, 2023, 08:58	solve the equation looks like heat conduction equation	#1
ythw New Member zw Join Date: Oct 2023 Posts: 1 Rep Power: 0	Hello, I want to use OenFOAM to solve a partial differential equation,which looks like heat conduction equation. But its "thermal diffusion coefficient" is less than 0. It is fvm::ddt(T) - fvm::laplacian(DT, T) == 0 But its Dt < 0. I tried to use laplacianFoam, but the calculation failed. "Floating point exception" appears. Can someone tell me how to adjust my laplacianFoam case, or which solver I should choose?

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October 27, 2023, 12:18		#2
Tobermory Senior Member Join Date: Apr 2020 Location: UK Posts: 747 Rep Power: 14	Is the equation not unstable with a negative diffusion coefficient, i.e. working as intended? Think of a simple case of 1D heat conduction in a bar with a negative heat diffusivity - any gradient would automatically try steepen instead of diffuse. So I can imagine that your solution would run away quickly, and ultimately crash.