Comparison: Finite Volume Method vs. Analytic Method
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: 120°C / 160°C / 200°C / 240°C / 280°C
Analytic Method: 121,8°C / 164,2°C / 205°C / 244,2°C / 281,8°C
Differences: 1,8°C / 4,2°C / 5°C / 4,2°C /1,8°C
(T0= 100°C; T6=300°C = 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 5°C. On both sides the differences get smaller.
My question is: How can I explain this effect? Why is the highest difference on node T3 (5°C) and why get the differences smaller on the start T1 and end T5 node.
I hope somebody can help me!
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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