Efficient simulation of transient gas networks using IMEX integration schemes and MOR methods

Modeling and Simulation of fluids in large networks are challenging problems. We provide an approach combining techniques in Model Order Reduction (MOR) and implicit-explicit (IMEX) integration to create efficient and stable simulations. Systems of gas flow in pipe networks are modeled as hyperbolic partial differential algebraic equations, which results after spatial discretization, in a nonlinear differential algebraic system. Standard techniques are slow in the best case, where in the worst case they are not even applicable to the system. This is due to several properties of said system, starting with the fact that it is a differential algebraic system, that it is nonlinear, and stiff. A first and major step in order to achieve stable and fast simulators for these problems is what we call the decoupling step. In that step, we are able to extract an ordinary differential equation which describes the inherent dynamic of the model. This step is only possible due to the chosen spatial discretization we use. Next, we use a Proper Orthogonal Decomposition (POD) and the Discrete Empirical Interpolation Method (DEIM) together with implicit-explicit (IMEX) integration method to reduce the size of the states and the number of time-steps. Using an integration method tailored to the problem is essential to being able to create transient simulation within a reasonable computation time. MOR methods, which further reduce the computation time are particularly important if we are interested in an optimization problem.