The name is absent



103


yields


ʌd ~vτ

Ax


vτ - Vww
∆.τ


where vτ is the voltage at the transition compartment. By (4.6) this implies


(4.8)

Although the implementation above is only first-order accurate, it can be improved
to second-order accuracy as described in §A.2. However, all the results in this thesis
were produced using the first-order scheme.

Discretizing the ∂xx terms in the above systems and substituting in for vr we
arrive at expressions for the voltages at the compartments adjacent to the transition
compartment:

∂χχV s


V2s - 2vs + VT

(ʌʃ)2

v2 — 2v1 + ɪvɪ 4- ɪv^
s           ' 2 s ' 2 vW

(∆x)2

v2 — -vɪ + l∙v^f,u

vs 2 S ' 2 W

(Ax)2

:Nw-l

W


lvɪ — -v^w 4

2 S 2vw ~

(Ax)2

This reveals the coupling between these two systems. Using the Hines ordering, I now

discretize (4.2)-(4.4) and the conditions given in (4.5) and (4.7) to arrive at



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