Speedup of water distribution simulation by domain decomposition

The Schur complement domain decomposition method is used for solution of large linear systems. The algorithm is based on the subdivision of the domain into smaller ones and the solution of those sub-domains independently. Regarding water distribution systems modeling, the hydraulic simulation could be formulated as a sequence of systems of linear equations. Therefore, this paper utilizes the domain decomposition method to accelerate the simulation process further. The method is evaluated using a large scale real-world system with 63,616 junctions and 64,200 pipes as case study. The case study shows that the methodology could improve the performance of hydraulic simulation app. by a factor of 8 without losing accuracy at a suitable level of domain decomposition. Although the optimal level of decomposition is case specific, considerable speedup might still be achievable by decomposing a large system into only a few subsystems. We utilizes a domain decomposition method to speed up water distribution simulation.The author's method is verified based on a large scale real world water distribution system.Compared with EPANET, the method could accelerate hydraulic simulation app. by a factor of 8 without losing accuracy.The method is general applicable to all solution methods of water distribution simulation.

[1]  Luigi Berardi,et al.  Computationally Efficient Modeling Method for Large Water Network Analysis , 2012 .

[2]  Andrea Toselli,et al.  Domain decomposition methods : algorithms and theory , 2005 .

[3]  Lindell Ormsbee,et al.  The History of Water Distribution Network Analysis: The Computer Age , 2008 .

[4]  Sequential and parallel domain decomposition methods for a singularly perturbed parabolic convection-diffusion equation , 2008 .

[5]  Boris Kompare,et al.  Environmental Modelling & Software , 2014 .

[6]  Lisa Scholten,et al.  Combining expert knowledge and local data for improved service life modeling of water supply networks , 2013, Environ. Model. Softw..

[7]  Bogumil Ulanicki,et al.  Parallel Computing in Water Network Analysis and Leakage Minimization , 2000 .

[8]  Mustafa M. Aral,et al.  Nodal Importance Concept for Computational Efficiency in Optimal Sensor Placement in Water Distribution Systems , 2007 .

[9]  Anthony J. Jakeman,et al.  Ten iterative steps in development and evaluation of environmental models , 2006, Environ. Model. Softw..

[10]  Uri Shamir,et al.  Water Distribution Systems Analysis , 1968 .

[11]  A. George Nested Dissection of a Regular Finite Element Mesh , 1973 .

[12]  Luigi Berardi,et al.  Assessing climate change and asset deterioration impacts on water distribution networks: Demand-driven or pressure-driven network modeling? , 2012, Environ. Model. Softw..

[13]  E. Todini,et al.  A gradient algorithm for the analysis of pipe networks , 1988 .

[14]  Jakobus E. van Zyl,et al.  Two-Point Linearization Method for the Analysis of Pipe Networks , 2008 .

[15]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .

[16]  R. Salgado,et al.  Extended gradient method for fully non-linear head and flow analysis in pipe networks , 1994 .

[17]  George Karypis,et al.  Multilevel k-way Partitioning Scheme for Irregular Graphs , 1998, J. Parallel Distributed Comput..

[18]  Hardy Cross,et al.  Analysis of flow in networks of conduits or conductors , 1936 .

[19]  Ezio Todini Towards Realistic Extended Period Simulations (EPS) in Looped Pipe Network , 2008 .

[20]  Pascal Hénon,et al.  A Parallel Direct/Iterative Solver Based on a Schur Complement Approach , 2008, 2008 11th IEEE International Conference on Computational Science and Engineering.

[21]  Vipin Kumar,et al.  A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs , 1998, SIAM J. Sci. Comput..

[22]  Janne Roos,et al.  Using METIS and hMETIS Algorithms in Circuit Partitioning , 2006 .

[23]  Güzin Bayraksan,et al.  Reclaimed water distribution network design under temporal and spatial growth and demand uncertainties , 2013, Environ. Model. Softw..

[24]  Joseph H. A. Guillaume,et al.  Characterising performance of environmental models , 2013, Environ. Model. Softw..

[25]  Avi Ostfeld,et al.  Topological clustering for water distribution systems analysis , 2011, Environ. Model. Softw..

[26]  Gabriel Kron,et al.  Diakoptics : the piecewise solution of large-scale systems , 1963 .

[27]  Aaron C. Zecchin,et al.  Steady-State Behavior of Large Water Distribution Systems: Algebraic Multigrid Method for the Fast Solution of the Linear Step , 2012 .

[28]  A. Brameller,et al.  Hybrid method for the solution of piping networks , 1971 .

[29]  Wolfgang Rauch,et al.  Automatic generation of water distribution systems based on GIS data , 2013, Environ. Model. Softw..

[30]  A. Cenedese,et al.  Optimal design of water distribution networks , 1978 .

[31]  Idel Montalvo,et al.  Sensitivity analysis to assess the relative importance of pipes in water distribution networks , 2008, Math. Comput. Model..

[32]  Julian Thornton,et al.  Water Loss Control , 2008 .

[33]  Pieter Crous Application of stream processing to hydraulic network solvers , 2011 .

[34]  J. E. van Zyl,et al.  The potential of graphical processing units to solve hydraulic network equations , 2012 .

[35]  Don J. Wood,et al.  Hydraulic Network Analysis Using Linear Theory , 1972 .

[36]  R. Epp,et al.  Efficient Code for Steady-State Flows in Networks , 1971 .

[37]  E. Todini,et al.  Unified Framework for Deriving Simultaneous Equation Algorithms for Water Distribution Networks , 2013 .

[38]  Andrzej J. Osiadacz Osiadacz,et al.  Simulation and Analysis of Gas Networks , 1987 .