Advanced Loop-flow Method for Fast Hydraulic Simulations Z. Vasilic - - PowerPoint PPT Presentation

Advanced Loop-flow Method for Fast Hydraulic Simulations

• Z. Vasilic1 / M. Stanic2 / Z. Kapelan3 / D. Prodanovic2

1 University of Belgrade, zvasilic@grf.bg.ac.rs 2 University of Belgrade 3 University of Exeter

OUTLINE

• Advanced Loop-flow method (TRIBAL-∆Q)
• Minimal basis loops identification alg.
• Efficient implementation of loop-flow method
• Examples, results & discussion
• Introduction
• Methods for hydraulic analysis
• Overview of Loop-flow method
• Conclusions

• Water Distribution Network (WDN)
• Purpose of Hydraulic simulation ?
• Essential prerequisite for any type of

general WDN analysis is Mathematical model of the WDN

• Modification of the existing WDN
• Expansion of the existing WDN
• Optimisation process is usually involved
• Need for the hydraulic simulation method

efficient in terms of computational speed

Multiple scenarios/alternatives

Optimization

Adopted solution

Result

INTRODUCTION

• Systematization of the methods

METHODS for HYDRAULIC ANALYSIS

• Ref. Todini & Rossman 2013
• Depending of the unknown variable:
• Q method
• H method
• ∆Q method (loop-flow)

Node based equations Loop based equations

GGA (EPANET)

• Node vs. Loop based methods

METHODS for HYDRAULIC ANALYSIS

BWSN2 Network – Large Network (Ostfeld et.al 2008): 14 831 Links 12 523 Nodes 2 308 Loops

Loop based Less number of unknowns (eqs) Solving branched network is easier (No iterative procedure) Node based Easy to „code“ (system

• f non-linear eqs.)

Don’t require loop identification

• Initial flows satisfy nodal continuity equations
• Loop head-loss equations are formed

Loop-flow (∆Q) method

         

1 ( ) ( ) 2 1 2 45 2 2 45 45 1 ( ) ( ) 52 2 2 52 52 1 ( ) ( ) 12 1 2 1 2 12 12 1 ( ) ( ) 41 2 2 41 41

, ... ... ...

n

• n
• n
• n
• f

Q Q R Q Q Q Q R Q Q Q Q R Q Q Q Q Q Q R Q Q Q Q

   

                           

• Non-linear system for the network

 

 

 

1 n T T T 

         

• f ΔQ

M R Q M ΔQ Q M ΔQ A H



 

Loop-flow (∆Q) method

• Non-linear system for the

network

 

 

 

1 n T T T 

         

• f ΔQ

M R Q M ΔQ Q M ΔQ A H



 

• NR Linearization of the

system yields iterative solution form

• 1

1 i i i i 

ΔQ = ΔQ - J f

• Structure of identified

loops has great influence

• n solver’s efficiency

4 loops X 4 links 2 loops X 4 links 2 loops X 6 links

TRIBAL – ∆Q method

• Combines:
• 1. New algortihm for optimal loop identification (TRIBAL)
• 2. Efficient implementation of loop-flow based hyd.solver (∆Q)
• TRIangulation BAsed Loops (TRIBAL) identification algorithm is

based on constrained Delaunay triangulation and Graph Theory

TRIBAL – ∆Q method

• TRIBAL algorithm

TRIBAL – ∆Q method

• TRIBAL – DQ method implementation

TRIBAL – ∆Q method

• TRIBAL – DQ method implementation (1st Block – Pre-processing)

• ENRunLoops uses:
• linsolve routine to solve

non-linear system

• newcoeff routine to

calculate links coeffs

TRIBAL – ∆Q method

• TRIBAL – DQ method implementation (2nd Block – Hyd. Simulation)

1 1

1

ij n ij ij ij

f Q nR Q

 

          

 

1 n ij ij ij k k

f nR Q Q Q



     ( , )

ij m ij m k k

f f m k Q Q



     



J

Data from the 1st Block

• newcoeff updates only links in loops

TRIBAL – ∆Q method

• TRIBAL – DQ method implementation (2nd Block – Hyd. Simulation)

BENCHMARKING RESULTS

BIN

Network Nn Nl Ns nRL nPL nL LF BIN 447 454 4 8 3 11 0.36 PES 71 98 3 28 2 30 0.96

• 2 Case study networks

PES

BENCHMARKING RESULTS

• Comparison criteria:

1. Computational efficiency (total time & speedup ) 2. Convergence (num of iter)

• Comparison is made between 3 solvers:

1. GGA solver – as implemented in EPANET 2. TRIBAL – DQ solver 3. ASL – DQ solver

• Reported calculation times are execution times for 2nd Block
• Times are averaged over 10 series of 10,000 cumulative runs
• Target convergence for the discharge is eps=10-3

( ) ( )

F

t GGA SPU t Q  

BENCHMARKING RESULTS

• Convergence
• Computational efficiency

6 6 6

GGA TRIBAL-DQ ASL-DQ

Number of Iterations BIN network

3.859 1.087 1.111 GGA TRIBAL-DQ ASL-DQ

Simulation time (s) BIN network DQ DQ DQ DQ

BENCHMARKING RESULTS

• Convergence
• Computational efficiency

6 6 6 5 7 7

GGA TRIBAL-DQ ASL-DQ

Number of Iterations BIN network PES network DQ DQ

3.859 1.087 1.111 0.712 0.563 0.675 GGA TRIBAL-DQ ASL-DQ

Simulation time (s) BIN network PES network DQ DQ

BENCHMARKING RESULTS

• Efficiency of loop-based solvers compared to GGA

1035 27 29 236 90 141 GGA TRIBAL-DQ ASL-DQ

NNZ elements in Cholesky factor BIN network PES network DQ DQ

3.551 3.475 1.265 1.055 TRIBAL-DQ ASL-DQ

SPUF (-) BIN network PES network DQ DQ

2.14 % 16.61 %

CONCLUSIONS

• New loop-flow based TRIBAL-DQ method is presented
• Computationally faster than GGA for steady state simulations
• Achieved speedups are result of:

1. Highly sparse solution matrix obtained with TRIBAL algorithm 2. Efficient implementation of DQ hydraulic solver

• Well suited for substantially branched networks
• Convenient for use in optimization tasks and networks with

unchanged topology

• Accounting flow control devices and pressure-driven analysis

Advanced Loop-flow Method for Fast Hydraulic Simulations

• Z. Vasilic1 / M. Stanic2 / Z. Kapelan3 / D. Prodanovic2

1 University of Belgrade, zvasilic@grf.bg.ac.rs 2 University of Belgrade 3 University of Exeter