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.