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The problem of solving transport equations with second-order transient terms

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Old   March 19, 2024, 09:27
Default The problem of solving transport equations with second-order transient terms
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wenbozhou
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Hi,
I had a problem defining additional variables using CFX. The transient term of the equation I need to solve is second-order, not a standard transport equation, so I want to know how to deal with this kind of problem using cfx.
Any suggestions would be greatly appreciated.
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Old   March 19, 2024, 16:42
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I cannot see an easy way of implementing that equation using the built in additional variables. I think you will have to model that using a user fortran routine you write yourself.

I would store the variable as an algebraic additional variable, but all the calculations on it would be done in user fortran.

This would not be easy to do, as you will have to develop a numerical scheme which converges and is stable and which intergates into the CFX structure.

Depending on how complex the rest of your model is you could consider modelling the whole system in something like matlab where you then have full control over the equations you are solving.
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Old   March 20, 2024, 06:29
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First of all, what equation are you solving?

Let us say your equation is:

\frac{\partial^2 \phi}{\partial t^2} = f(t)

You can break it up into two equations of 1st-order by

\frac{\partial \phi}{\partial t} = \psi

\frac{\partial \psi}{\partial t} = f(t)

This will let the solver deal with them, but the solver does not know they are connected, and depending on the nature of the transient, the numerical stencil of splitting the 2nd-order time derivative may bring some truncation errors.
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Old   March 20, 2024, 07:34
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Quote:
Originally Posted by ghorrocks View Post
I cannot see an easy way of implementing that equation using the built in additional variables. I think you will have to model that using a user fortran routine you write yourself.

I would store the variable as an algebraic additional variable, but all the calculations on it would be done in user fortran.

This would not be easy to do, as you will have to develop a numerical scheme which converges and is stable and which intergates into the CFX structure.

Depending on how complex the rest of your model is you could consider modelling the whole system in something like matlab where you then have full control over the equations you are solving.
Thank you for your comments.

The equation is not complicated except for the transient term, where the "omega" in the source term is the vorticity vector and "u" is the velocity vector.

I've read the user help documentation and there doesn't seem to be any mention of changes to transient items in additional variables.

Therefore, I am considering using Fortran to solve this equation.
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Old   March 20, 2024, 07:43
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Quote:
Originally Posted by Opaque View Post
First of all, what equation are you solving?

Let us say your equation is:

\frac{\partial^2 \phi}{\partial t^2} = f(t)

You can break it up into two equations of 1st-order by

\frac{\partial \phi}{\partial t} = \psi

\frac{\partial \psi}{\partial t} = f(t)

This will let the solver deal with them, but the solver does not know they are connected, and depending on the nature of the transient, the numerical stencil of splitting the 2nd-order time derivative may bring some truncation errors.
This seems like a solution, and I'm going to try it. Thank you very much for your comments.
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