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Comparison: Finite Volume Method vs. Analytic Method

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Old   March 5, 2010, 08:39
Default Comparison: Finite Volume Method vs. Analytic Method
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Hi,
at the moment I'm writing an assessment and need some help. The problem is to calculate the steady state temperature using the finite volume method in a plate. In addition, the results of the finite volume method should be compared to the exact analytical solution.

The following chart shows the results of each calculation method and the difference between them:

Temperature on node Tx: T1 T2 T3 T4 T5
Finite Volume Method: 120C / 160C / 200C / 240C / 280C
Analytic Method: 121,8C / 164,2C / 205C / 244,2C / 281,8C
Differences: 1,8C / 4,2C / 5C / 4,2C /1,8C

(T0= 100C; T6=300C = Known surface temperature)

The Chart shows that the values of the differences get some symmetrical characteristics (1,8; 4,2; 5; 4,2; 1,8). The highest difference is to find on temperature T3 with 5C. On both sides the differences get smaller.

My question is: How can I explain this effect? Why is the highest difference on node T3 (5C) and why get the differences smaller on the start T1 and end T5 node.

I hope somebody can help me!

Best regards,

m-fry
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Old   April 20, 2010, 14:40
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Kiril Shterev
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The reason is order of accuracy of the approximation
If You use more control volumes (close to infinity) two solution have to coinside.
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