Solving Natural Distribution Ventilation Network with Homotopy Method

The solution of natural distribution ventilation network is the basis of ventilation network optimization, The essence of the solution is to calculate nonlinear equations with Newton method at present, The calculating precision or calculating time is influenced heavely by the initial value selection when Newton method is used. In order to solve the limitations of Newton method, a common algorithm to solve non-linear equation system–homotopy method–was discussed and the homotopy equation for solving natural distribution ventilation network was built. A ventilation network case was solved with free software–Octave–in this paper. Based on the discussion above, the relationships among initial value choice, numerical integral step and calculating precision were discussed when this method was used. The results show that homotopy method is an effective way for solving natural distribution ventilation network. In addition, solving ventilation network with Octave can effectively avoid the copyright problem which is often caused when program language such as Matlab and VB are used to solve the ventilation network.