摘要：Since the equations that are involved in the behaviour of a flow distribution . network form a non-linear system, it can be described mathematically through matrixes and solved with the iterative Newton - Raphson method. When stating this problem, each node of the network would be connected to a few pipes thus resulting in a sparsed coefficient matrix. Therefore the resultant system is easily solved. However, in most current cases, the nodes may have a great connectivity grade and the sparseness of the coefficient matrix is an important factor. Due to this fact, the bandwidth of the matrix should be reduced in order to obtain a quick solution of the system. Here, the theory of graphs is applied to describe a steady state network topology clearly and systematically and an algorithm for labelling the graph -based on Jeppson and Davis method- is proposed. Such algorithm allows the concentration of elements close to the main diagonal and the computer time and effort are therefore saved. Some simple examples of its application are shown so as to explain how the algorithm is developed.
其他摘要：Since the equations that are involved in the behaviour of a flow distribution . network form a non-linear system, it can be described mathematically through matrixes and solved with the iterative Newton - Raphson method. When stating this problem, each node of the network would be connected to a few pipes thus resulting in a sparsed coefficient matrix. Therefore the resultant system is easily solved. However, in most current cases, the nodes may have a great connectivity grade and the sparseness of the coefficient matrix is an important factor. Due to this fact, the bandwidth of the matrix should be reduced in order to obtain a quick solution of the system. Here, the theory of graphs is applied to describe a steady state network topology clearly and systematically and an algorithm for labelling the graph -based on Jeppson and Davis method- is proposed. Such algorithm allows the concentration of elements close to the main diagonal and the computer time and effort are therefore saved. Some simple examples of its application are shown so as to explain how the algorithm is developed.
