Natural gas production and distribution in the US is interconnected continent-wide, and hence the simulation of fluid flow in pipeline networks is a problem of scientific interest. While the problem of steady, unidirectional flow of fluid in a single pipeline is simple, it ceases to be so when we consider fluid flow in a large network of pipelines. The resultant system of nonlinear equations depends on the grid topology and while it has been shown that the system has a unique solution, there is no numerical algorithm that offers guaranteed convergence to the solution.

For small network sizes, the sequence of Newton-Raphson iterates converges in numerical experiments, and with suitable nondimensionalization, it does so even for networks of moderate size. However, for very large networks, the initial guesses we provide could lie outside the basin of attraction of the Newton-Raphson algorithm and consequently, it may fail to converge.

It would be advantageous if the solution of the large nonlinear system could be achieved by solution of smaller nonlinear sub-systems wherein the Newton algorithm is more likely to succeed. In this talk, I will describe such a procedure, an hierarchical network partitioning algorithm that enables the solution of such large nonlinear systems. The fundamental idea that underpins the method is one that can be exploited gainfully in network flow problems relevant to another application or context.