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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