# Comparison: Finite Volume Method vs. Analytic Method

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 March 5, 2010, 07:39 Comparison: Finite Volume Method vs. Analytic Method #1 New Member   Join Date: Mar 2010 Posts: 1 Rep Power: 0 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: 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! Best regards, m-fry

 April 20, 2010, 14:40 #2 New Member     Kiril Shterev Join Date: Jan 2010 Location: Sofia, Bulgaria Posts: 2 Blog Entries: 1 Rep Power: 0 The reason is order of accuracy of the approximation If You use more control volumes (close to infinity) two solution have to coinside.