Efficient Numerical Methods for Gas Network Modeling and Simulation
This work addresses the need for faster simulation of gas networks, which is important for engineers and operators, but the improvements are incremental.
The paper develops efficient numerical methods for simulating transient dynamics in gas pipeline networks, reducing algebraic constraints and exploiting block lower triangular structure to create an efficient preconditioner, achieving faster simulations on benchmark problems.
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.