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

wenbozhou · March 19, 2024, 09:27

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.

ghorrocks · March 19, 2024, 16:42

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.

Opaque · March 20, 2024, 06:29

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.

wenbozhou · March 20, 2024, 07:34

Quote:

Originally Posted by ghorrocks

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.

wenbozhou · March 20, 2024, 07:43

Quote:

Originally Posted by Opaque

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.

March 19, 2024, 16:42		#2
ghorrocks Super Moderator Glenn Horrocks Join Date: Mar 2009 Location: Sydney, Australia Posts: 17,703 Rep Power: 143	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. __________________ Note: I do not answer CFD questions by PM. CFD questions should be posted on the forum.

March 20, 2024, 06:29		#3
Opaque Senior Member Join Date: Jun 2009 Posts: 1,804 Rep Power: 32	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. __________________ Note: I do not answer CFD questions by PM. CFD questions should be posted on the forum.

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