Modeling the dynamics of flow in gas pipelines
The description of nonstationary one-dimensional flow of a nonideal gas in a pipe is treated with the goal of developing a mathematical description of flow and pressure (density) dynamics adequate for creating a simulation model of large pipeline networks, the analysis starts from Newton's equation of motion. The continuity equation, and the energy equation. The authors determine the relationships among: space discretization, terms of Newton's equation, and frequency of the dynamic processes occurring in the system. The resulting dynamic description of a pipe is discussed for two different modes of space discretization, and quantitative rules for space discretization are given.
On PDE solution in transient optimization of gas networks
Operative planning in gas distribution networks leads to large-scale mixed-integer optimization problems involving a hyperbolic PDE defined on a graph. We consider the NLP obtained under prescribed combinatorial decisions-or as relaxation in a branch-and-bound framework, addressing in particular the KKT systems arising in primal-dual interior methods. We propose a custom solution algorithm using sparse projections locally in time, based on the KKT systems' structural properties in space as induced by the discretized gas flow equations in combination with the underlying network topology. The numerical efficiency and accuracy of the algorithm are investigated, and detailed computational comparisons with a previously developed control space method and with the multifrontal solver MA27 are provided.
Description of a Sparse Matrix Compiler with Applications
Abstract : The report describes the operation and use of a number of computer programs that generate code for the manipulation of sparse matrices. In particular, code generators are described for the efficient repetitive solution of simultaneous linear equations which have a common sparsity structure. Applications to a variety of engineering problems are given. (Author)