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May 3, 2013, 06:07 
discretisation

#1 
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ramin abedifard
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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 
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Filippo Maria Denaro
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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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May 3, 2013, 17:52 

#4 
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Filippo Maria Denaro
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May 4, 2013, 03:16 

#5 
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ramin abedifard
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May 4, 2013, 04:57 

#6 
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Filippo Maria Denaro
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May 4, 2013, 07:13 

#7 
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ramin abedifard
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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 
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Filippo Maria Denaro
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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 timespace derivatives usually appears when you use some timeintegration method of the class of the LaxWendroff. 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:
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:
Again, the real problem is not in the discretization of a single term (is quite simple to do on a timespace 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 nonlinear other requirements can be necessary. 

May 5, 2013, 05:44 

#11  
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ramin abedifard
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