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Implementing boundary condition as additional term in differential equations

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Old   March 16, 2015, 12:32
Default Implementing boundary condition as additional term in differential equations
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Manuel do Nascimento
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Hello,

I am wondering if there is anyone who did something like this (sorry for bad english):

let's say we have a one dimensional heat convection problem dT/dt = a*dT/dx.

Now let's say one boundary is supposed to be adiabatic -> dT/dx = 0.

The idea: I would like to implement the boundary condition as an additional term in the differential equation with the following method: dT/dt = a*dT/dx + A*(dT/dx)

Now the factor A has to have a value equal to zero (or extremely small) in any area, except at (or very near) the adiabatic wall where it has to have a large value. The large value of A then has the function to make sure the boundary condition is satisfied at this area to make the product in the new differential equation equal to zero.

This is just an imaginary example to get the idea. I think this method already exists but I don't know the name or how to find it in a mathematical publication.

Does anyone know a solver / a case where something like this has been done? Or an idea how to implement this in OpenFOAM? I am quite new to this software.

Best regards, and thanks
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Old   March 25, 2015, 12:48
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Mat
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Hi Manuel,

I think what you want to do is close to a penalization method, which is part of the family of immersed boundary methods or fictitious domain method. (You will find a lot of article for those methods in literature)

But first of all, why don't you want to use a normal boundary condition for your temperature gradient ?

Best,
Mat
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