Newton-Raphson algorithm initial guesses

Figure 3-23. The Newton-Raphson algorithm with an unfortunate initial guess.

Invariably the flow network will form part of a larger model, which will define the boundary pressures. These will remain fixed during the process of iteration. The basic strategy is to use initial guesses of the pressures at the intermediate nodes and, in some cases, of the nodal temperatures or specific volumes, in order to calculate the flows and then to see if they balance. The guesses will then be refined successively using an algorithm such as Newton-Raphson until the flows balance to a predetermined tolerance. 

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