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except those adjacent to the transition compartment.
Consider first the adjacent strong compartment. Discretizing at this compartment
yields
⅛((as^)2⅛v^) = + 2afτ¾af''a,v'vr
∕a^rT')2
⅛-l[v^÷1-2v^ + vr]+2a^
a^+1 - aτ
2∆τ
vsτ+1 ~ vτ
2∆τ
where ay is the radius of the transition compartment. After substituting in (??)
for vʃ, followed by much tedious algebra and gathering like terms, we arrive at the
following expressions for the voltage coefficients:
⅛((afη2¾vfr) ≈ vs^+1
('aʌ'ʃi2 a^,τ
—⅛—— -I--≡---( a∕vτ+l _ a„ j
(ʌʃ)2 2(∆rr)2 V s T)
|
+ vfτ |
4 (aw∏2 a^τ --± s. / + -⅛---(a _ aJVτ+l 2 (∆τ)2 4(∆x)2 *∙ τ s |
) |
|
+ v"- |
1 Γa^rrl2 ʌl -s У ■ + -⅛---(aτ - ajvτ+1') [2(∆τ)2 4(∆z)2k τ s , |
__ λ, ,rNτ+^L I v ..Nt I ^Wu.
— Xs,lvs + Xs,2vs + Xs,3vω ,
where χs,1, ‰ι2, and χs,3 are the coefficients of the voltage terms. Similarly, for the