Finite difference method for charge calculation
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- 1. Name :- Smit Shah -140410109096 T.Y Electrical 2 Sem 6 Subject:-High Voltage Engineering Topic :-Finite Difference Method For Charge Calculation 1
- 2. FINITE DIFFERENCE In numerical analysis, two different approaches are commonly used: The finite difference and the finite element methods. In heat transfer problems, the finite difference method is used more often and will be discussed here. The finite difference method involves: Establish nodal networks Derive finite difference approximations for the governing equation at both interior and exterior nodal points Develop a system of simultaneous algebraic nodal equations Solve the system of equations using numerical schemes 2
- 5. Finite Difference Approximation cont. 5
- 6. Finite Difference Approximation cont. 6
- 7. A System of Algebraic Equations 7
- 9. Summary of nodal finite-difference relations for various configurations: 9 Case 1 Interior Node 04TTTTT nm,n1,mn1,m1nm,1nm,
- 10. Case 2 Node at an internal corner with convection 10 1, , 1 1, , 1 ,2( ) ( ) 2 2(3 ) 0m n m n m n m n m n h x h x T T T T T T k k
- 11. Case 3 Node at a plane surface with convection 11 1, , 1 , 1 ,(2 ) 2 2( 2) 0m n m n m n m n h x h x T T T T T k k
- 12. Case 4 Node at an external corner with convection 12 , 1 1, ,( ) 2 2( 1) 0m n m n m n h x h x T T T T k k
- 13. Case 5 Node at a plane surface with uniform heat flux 13 04 ''2 )2( ,1,1,,1 nmnmnmnm T k xq TTT
- 14. 14