  We study the modeling and simulation of gas pipeline networks, with a focus
on fast numerical methods for the simulation of transient dynamics. The
obtained mathematical model of the underlying network is represented by a
nonlinear differential algebraic equation (DAE). With our modeling, we reduce
the number of algebraic constraints, which correspond to the $(2,2)$ block in
our semi-explicit DAE model, to the order of junction nodes in the network,
where a junction node couples at least three pipelines. We can furthermore
ensure that the $(1, 1)$ block of all system matrices including the Jacobian is
block lower triangular by using a specific ordering of the pipes of the
network. We then exploit this structure to propose an efficient preconditioner
for the fast simulation of the network. We test our numerical methods on
benchmark problems of (well-)known gas networks and the numerical results show
the efficiency of our methods.
