Mathematical software for gas transmission networks
This thesis is concerned with the development of numerical software for the simulation of gas transmission networks. This involves developing software for the solution of a large system of stiff differential/algebraic equations (DAE) containing frequent severe disturbances. The disturbances arise due to the varying consumer demands and the operation of network controlling devices such as the compressors. Special strategies are developed to solve the DAE system efficiently using a variable-step integrator. Two sets of strategies are devised; one for the implicit methods such as the semi-implicit Runge-Kutta method, and the other for the linearly implicit Rosenbrock-type method. Four integrators, based on different numerical methods, have been implemented and the performance of each one is compared with the British Gas network analysis program PAN, using a number of large, realistic transmission networks. The results demonstrate that the variable-step integrators are reliable and efficient. An efficient sparse matrix decomposition scheme is developed to solve the large, sparse system of equations that arise during the integration of the DAE system. The decomposition scheme fully exploits the special structure of the coefficient matrix. Lastly, for certain networks, the existing simulation programs fail to compute a feasible solution because of the interactions of the controlling devices in the network. To overcome this difficulty, the problem is formulated as a variational inequality model and solved numerically using an optimization routine from the NAG library (NAGFLIB(l982)). The reliability of the model is illustrated using three test networks.