# discretisation

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 May 3, 2013, 06:07 discretisation #1 New Member   ramin abedifard Join Date: Jul 2012 Posts: 12 Rep Power: 5 Hello I want to discretise one term of non fourier heat transfer equation with volume control method. I try to do it, but i cant. this term is: d2(cp u T)/(dt dx) that we have cp(T),u(x,y,t),T(x,y,t) T:temperate t:time thank you Last edited by ramin; May 3, 2013 at 16:32.

 May 3, 2013, 08:34 #2 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 1,605 Rep Power: 23 I have some doubt about your symbolism, you are referring to as a first time derivative or a second mixed x,t derivative....?

May 3, 2013, 16:40
#3
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ramin abedifard
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Quote:
 Originally Posted by FMDenaro I have some doubt about your symbolism, you are referring to as a first time derivative or a second mixed x,t derivative....?
sorry, d2(cp u T)/(dt dx)

May 3, 2013, 17:52
#4
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Filippo Maria Denaro
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Quote:
 Originally Posted by ramin sorry, d2(cp u T)/(dt dx)

what equation you are solving?

May 4, 2013, 03:16
#5
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ramin abedifard
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Quote:
 Originally Posted by FMDenaro what equation you are solving?
I said, non fourier heat transfer equation

May 4, 2013, 04:57
#6
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Filippo Maria Denaro
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Quote:
 Originally Posted by ramin I said, non fourier heat transfer equation
I never worked on such model, what about the mathematical classification of this equation?

May 4, 2013, 07:13
#7
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ramin abedifard
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Quote:
 Originally Posted by FMDenaro I never worked on such model, what about the mathematical classification of this equation?
It is a hyperbolic heat transfer equation. It should be discretised base on versteegَ s book(An introduction to computational fluid dynamics) and with volume control method.

 May 4, 2013, 13:46 #8 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 1,605 Rep Power: 23 Your question is not clear to me... to the best of my knowledge, a term like d2T/dxdt never appears in the original heat equation.... hybrid time-space derivatives usually appears when you use some time-integration method of the class of the Lax-Wendroff. But in such cases, the original equation is substituted into the derivative.

May 4, 2013, 18:26
#9
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ramin abedifard
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Quote:
 Originally Posted by FMDenaro Your question is not clear to me... to the best of my knowledge, a term like d2T/dxdt never appears in the original heat equation.... hybrid time-space derivatives usually appears when you use some time-integration method of the class of the Lax-Wendroff. But in such cases, the original equation is substituted into the derivative.
I want to write a computer program to solve my equation that one of the itُs terms is d2(cp u T)/(dtdx). Now i want to approximate this term base on my method that i said.
This term is very small, since it has a very small fixed coefficient. This coefficient shows the speed of heat propagation is not infinite.

May 5, 2013, 04:13
#10
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Filippo Maria Denaro
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Quote:
 Originally Posted by ramin I want to write a computer program to solve my equation that one of the itُs terms is d2(cp u T)/(dtdx). Now i want to approximate this term base on my method that i said. This term is very small, since it has a very small fixed coefficient. This coefficient shows the speed of heat propagation is not infinite.

Again, the real problem is not in the discretization of a single term (is quite simple to do on a time-space grid) but care in the discretization of the model equation is required.
You said it is hyperbolic, therefore the discretization of the whole model must be stable and accurate, but if the equation is also non-linear other requirements can be necessary.

May 5, 2013, 05:44
#11
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ramin abedifard
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Quote:
 Originally Posted by FMDenaro Again, the real problem is not in the discretization of a single term (is quite simple to do on a time-space grid) but care in the discretization of the model equation is required. You said it is hyperbolic, therefore the discretization of the whole model must be stable and accurate, but if the equation is also non-linear other requirements can be necessary.
Yes, you are right, but the most important of my problem is the discretization of this term. May you send me your email to give whole of my equation.

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