OPTIMIZATION TECHNIQUE FOR SOLVING STEADY FLOWS IN LARGE NETWORK PIPE SYSTEMS
Masashi SHIMADA · Doboku Gakkai Ronbunshu · 1986
This paper deals with the loop analysis for efficiently solving the steady flow in large pipe network system. (1) The analysis having not flow rates through co-trees but around loops (or meshes) as independent variables is graph-theoretically formulated. (2) The calculation algorithm using the conjugate gradient method is shown to solve the nonlinear optimization problem based on the principle of minimum dissipative energy. (3) For practical and efficient calculations of sparse matrices how to number nodes, trees, and fundamental loops is made clear. And (4) the method due to the minimization is compared with other excellent methods based on the Newton-Raphson algorithm.