Finite difference method for charge calculation

Name :- Smit Shah -140410109096

T.Y Electrical 2 Sem 6

Subject:-High Voltage Engineering

Topic :-Finite Difference Method For

Charge Calculation 1

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 networksDerive finite difference approximations for the governing

equation at both interior and exterior nodal pointsDevelop a system of simultaneous algebraic nodal equationsSolve the system of equations using numerical schemes

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The Nodal Networks

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Finite Difference Approximation

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Finite Difference Approximation cont.

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Finite Difference Approximation cont.

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A System of Algebraic Equations

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Matrix Form

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Summary of nodal finite-difference relations forvarious configurations:

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Case 1 Interior Node

04TTTTT nm,n1,mn1,m1nm,1nm,

Case 2 Node at an internal corner with convection

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1, , 1 1, , 1 ,2( ) ( ) 2 2(3 ) 0m n m n m n m n m n

h x h xT T T T T T

k k

Case 3 Node at a plane surface with convection

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1, , 1 , 1 ,(2 ) 2 2( 2) 0m n m n m n m n

h x h xT T T T T

k k

Case 4 Node at an external corner with convection

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, 1 1, ,( ) 2 2( 1) 0m n m n m n

h x h xT T T T

k k

Case 5 Node at a plane surface with uniform heat

flux

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04''2

)2( ,1,1,,1

nmnmnmnm Tk

xqTTT

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