Numerical Methods for Uncertainty Quantification in Gas Network Simulation

Abstract

When modeling the gas flow through a network, some elements such as pressure control valves can cause kinks in the solution. In this thesis we modify the method of simplex stochastic collocation such that it is applicable to functions with kinks. First, we derive a system of partial differential and algebraic equations describing the gas flow through different elements of a network. Restricting the gas flow to an isothermal and stationary one, the solution can be determined analytically. After introducing some common methods for the forward propagation of uncertainty, we present the method of simplex stochastic collocation to approximate functions of uncertain parameters. By utilizing the information whether a pressure regulator is active or not in the current simulation, we improve the method such that we can prove algebraic convergence rates for functions with kinks. Moreover, we derive two new error estimators for an adaptive refinement and show that multiple refinements are possible. Conclusively, several numerical results for a real gas network are presented and compared with standard methods to demonstrate the significantly better convergence results.