Pupping rate optimization in a storm drainage system through the combined use of numerical simulation and linear programming

Abstract A problem consisting of the determination of the optimal discharge hydrograph of a pumping station located at the downstream end of a storm drainage channel subject to time-varying inflow, is described. The goal of the pumping station operational strategy is to always maintain the minimum amount of water stored in the channel by maximizing the instantaneous pumped flow rate. The equations of water motion in the channel and the design and operational constraints are approximated by employing a quasilinear time integration scheme and a staggered spatial discretization. The resulting discrete equations are linear in the unknown values of the flow variables. Accordingly, the computation of the optimal pumped flow rate is formulated as a linear programming problem for each time step. An efficient solution algorithm is developed on the basis of the particular structure of the dynamic and operational constraints associated with the problem of interest. A numerical example that illustrates the application of the proposed procedure is presented.

[1]  R. F. Warming,et al.  An implicit finite-difference algorithm for hyperbolic systems in conservation-law form. [application to Eulerian gasdynamic equations , 1976 .

[2]  F. Henderson.  Open channel flow , 1966 .

[3]  H. Schwarz.  Numerical analysis of symmetric matrices , 1974 .

[4]  Edward A. McBean,et al.  Application of nonlinear optimization to water quality , 1987 .

[5]  Ismael Herrera,et al.  Numerical Modeling in Science and Engineering , 1988 .

[6]  T. S. Chau,et al.  Combining flow simulation and optimization for dynamic management of relief wells , 1989 .

[7]  Optimization of closure operations in a tidal basin during a storm-surge , 1987 .

[8]  V. T. Chow.  Open-channel hydraulics , 1959 .

[9]  T. Watanatada.  Least-Cost Design of Water Distribution Systems , 1973 .

[10]  Rodolfo Soncini Sessa,et al.  Modelling and Control of River Quality , 1979 .

[11]  John M. Mulvey,et al.  Designing optimal strategies for contaminated groundwater remediation , 1986 .

[12]  J. Cunge,et al.  Practical aspects of computational river hydraulics , 1980 .

[13]  B. Herrling,et al.  Coupling of finite element and optimization methods for the management of groundwater systems , 1986 .

[14]  A. J. Raudkivi,et al.  Loose Boundary Hydraulics , 2020 .

[15]  Robert E. Beck,et al.  Elementary Linear Programming with Applications , 1979 .

[16]  R. F. Warming,et al.  An Implicit Factored Scheme for the Compressible Navier-Stokes Equations , 1977 .

[17]  U. Shamir,et al.  Design of optimal water distribution systems , 1977 .

[18]  John M. Mulvey,et al.  Combining physical containment with optimal withdrawal for contaminated groundwater remediation , 1987 .