A Completely Parallel Scheme for Simulation of Transients in Large Gas Transmission Networks
A new method for digital simulation of transient pressure and flow in large gas transmission networks is presented. The method is also applicable to other processes with similar system’s properties. Our simulation method is based on a network-oriented partitioning of a large set of nonlinear equations, which has to be solved at every time step. By multiple utilization of certain (coupling)-equations a simple parallel block-iteration scheme can be formulated for the solution of the nonlinear equations. The block-iteration is based on the Newton/Raphson method combined with a linear block-iteration of the Jacobi type. All blocks of equations can be treated concurrently, while the amount of data exchange between the blocks remains comparatively low.
The new numerical scheme is ideally suited for efficient implementation on a parallel computing facility of MIMD-type. The assumptions that assure its applicability are discussed in detail. Rate of convergence and overall expense of computing power for the solution scheme are demonstrated by results from the simulation of a medium-sized gas transmission network.
KeywordsIteration Step Parallel Method Newton Step Coupling Variable Parallel Computer System
Unable to display preview. Download preview PDF.
- Berzins, M., Buckley, T.F., Dew, P.M. Systolic matrix iterative algorithms, in Parallel Computing 83, edited by M. Feilmeier and U. Schendel, North Holland Publications, Amsterdam-New York (1984).Google Scholar
- Crorkin, W., Allidina, A.Y., Malinowski, K., Singh, M.G. Decomposition-coordination techniques for parallel simulation — Part 2, Control Systems Centre Report No. 600, UMIST, Manchester, (1984).Google Scholar
- David, J.E. Iterative methods for sparse matrices, rn Sparsity and its Application, ed. by David, J.E., Cambridge University Press, (1985).Google Scholar
- Lappus, G., Schmidt, G. Supervision and control of gas transportation and distribution systems, 6th IFAC/IFIP Conference on Digital Computer Applications to Process Control, Dusseldorf, (1980).Google Scholar
- Malinowski, K., Allidina, A.Y., Singh, M.G., Crorkin, W.D. Decomposition-coordination techniques for parallel simulation part 1, Control Systems Centre Report No. 599, UMIST, Manchester, (1984).Google Scholar
- Peters, F.J. Parallelism and sparse linear equations, in Sparsity and its Applications, ed. by David, J.E., Cambridge University Press, (1985).Google Scholar
- Schmidt, G. The role of multi-microcomputers in automatic control, Proc. of the 4th Intern. Conference on Analysis and Optimization of Systems, Versailles, (1980).Google Scholar
- Tai, H.M., Sueks, R. Parallel system simulation, IEEE Trans, on Systems and Cybernetics, vol. SMC-14, No. 2, 177–183.Google Scholar
- Varga, R.S. Matrix iterative analysis, Prentice Hall, Englewood Cliffs, (1962).Google Scholar
- Weimann, A. Modellierung und Simulation der Dynamik von Gasverteilnetzen im Hinblick auf Gasnetzfuhrung und Gasnetzu-berwachung, Dissertation, Techn. Universität München, (1978).Google Scholar