Generic Construction and Efficient Evaluation of Flow Network DAEs and Their Derivatives in the Context of Gas Networks

We present a concept that provides an efficient description of differential-algebraic equations (DAEs) describing flow networks which provides the DAE function \(f\) and their Jacobians in an automatized way such that the sparsity pattern of the Jacobians is determined before their evaluation and previously determined values of \(f\) can be exploited. The user only has to provide the network topology and local function descriptions for each network element. The approach uses automatic differentiation (AD) and is adapted to switching element functions via the abs-normal-form (ANF).