Computer simulation of the Volga river hydrological regime: problem of water-retaining dam optimal location

E. O. Agafonnikova   ; A. Yu. Klikunova   ; A. V. Khoperskov

Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 10 (2017) no. 3, pp. 148-155

Résumé

We investigate of a special dam optimal location at the Volga river in the area of the Akhtuba left sleeve beginning (7 km to the south of the Volga Hydroelectric Power Station dam). We claim that a new water-retaining dam can resolve the key problem of the Volga-Akhtuba floodplain related to insufficient water amount during spring floodings due to the overregulation of the Lower Volga. Using a numerical integration of Saint-Vanant equations we study the water dynamics across the northern part of the Volga-Akhtuba floodplain taking into account its actual topography. As the result we found an amount of water $V_A$ passing to the Akhtuba during spring period for a given water flow through the Volga Hydroelectric Power Station (so-called hydrograph which characterises the water flow per unit of time). By varying the location of the water-retaining dam $ x_d, y_d $ we obtained various values of $V_A (x_d, y_d) $ as well as various flow spatial structure on the territory during the flood period. Gradient descent method provides the dam coordinated with the maximum value of ${V_A}$. Such approach to the dam location choice let us find the best solution, that the value $V_A$ increases by a factor of 2. Our analysis demonstrates a good potential of the numerical simulations in the field of hydraulic works.

Détail

Keywords: hydrodynamic simulation; Saint-Venant equations; numerical model; optimization; hydrology.

Bibliographie

[1] Khrapov S., Pisarev A., Kobelev I., Zhumaliev A., Agafonnikova E., Losev A., Khoperskov A., “The Numerical Simulation of Shallow Water: Estimation of the Roughness Coefficient on the Flood Stage”, Advances in Mechanical Engineering, 5 (2013), 1–11 | DOI

[2] Middelkoop H., Alabyan A. M., Babich D. B., Ivanov V. V., “Post-Dam Channel and Floodplain Adjustment Along the Lower Volga River, Russia”, Geomorphic Approaches to Integrated Floodplain Management of Lowland Fluvial Systems in North America and Europe, Springer, 2015, 245–264 | DOI

[3] Ladjel M., “Lamination Method of Flood Wadis and Projection of the Laminated Flood Hydrograph”, Journal of Fundamental and Applied Sciences, 8:1 (2016), 83–91 | DOI

[4] Gorski K., van den Bosch L. V., van de Wolfshaar K. E., Middelkoop H., Nagelkerke L. A. J., Filippov O. V. et al., “Post-Damming Flow Regime Development in a Large Lowland River (Volga, Russian Federation): Implications for Floodplain Inundation and Fisheries”, River Research and Applications, 28:8 (2012), 1121–1134 | DOI

[5] Voronin A. A., Eliseeva M. V., Khrapov S. S., Pisarev A. V., Khoperskov A. V., “The Regimen Control Task in The Eco-Economic System “Volzhskaya Hydroelectric Power Station – the Volga-Akhtuba Floodplain”. II. Synthesis of Control System”, Control Sciences, 2012, no. 6, 19–25 (in Russian)

[6] Chen D., Li R., Chen Q., Cai D., “Deriving Optimal Daily Reservoir Operation Scheme with Consideration of Downstream Ecological Hydrograph Through a Time-Nested Approach”, Water Resources Management, 29:9 (2015), 3371–3386 | DOI

[7] Haghighi A. T., Kløve B., “Development of Monthly Optimal Flow Regimes for Allocated Environmental Flow Considering Natural Flow Regimes and Several Surface Water Protection Targets”, Ecological Engineering, 82 (2015), 390–399 | DOI

[8] Borsche R., Klar A., “Flooding in Urban Drainage Systems: Coupling Hyperbolic Conservation Laws for Sewer Systems and Surface Flow”, International Journal for Numerical Methods in Fluids, 76 (2014), 789–810 | DOI | MR

[9] Voronin A. A., Vasilchenko A. A., Pisarev A. V., Khrapov S. S., Radchenko Yu. E., “Designing Mechanisms of the Hydrological Regime Management of the Volga-Akhtuba Floodplain Based on Geoinformation and Hydrodynamic Modelling”, Science Journal of Volgograd State University. Mathematics. Physics, 2016, no. 1(32), 24–37 (in Russian) | DOI

[10] Izem N., Seaid M., Wakrim M., “A Discontinuous Galerkin Method for Two-Layer Shallow Water Equations”, Mathematics and Computers in Simulation, 120 (2016), 12–23 | DOI | MR

[11] Bulatov O. V., Elizarova T. G., “Regularized Shallow Water Equations for Numerical Simulation of Flows with a Moving Shoreline”, Computational Mathematics and Mathematical Physics, 56:4 (2016), 661–679 | DOI | MR | Zbl

[12] D'yakonova T. A., Khoperskov A. V., Khrapov S. S., “Numerical Model of Shallow Water: the Use of GPUs NVIDIA CUDA”, Communications in Computer and Information Science, 687 (2017), 132–145 | DOI

[13] Khrapov S. S., Khoperskov A. V., Kuz'min N. M., Pisarev A. V., Kobelev I. A., “A Numerical Scheme for Simulating the Dynamics of Surface Water on the Basis of the Combined SPH-TVD Approach”, Numerical Methods and Programming, 12 (2011), 282–297 (in Russian)

[14] Khrapov S. S., Kuzmin N. M., Butenko M. A., “The Comparison of Accuracy and Convergence for the CSPH-TVD Method and Some Eulerian Schemes for Solving Gas-Dynamic Equations”, Science Journal of Volgograd State University. Mathematics. Physics, 2016, no. 6(37), 166–173 (in Russian) | DOI

[15] D'yakonova T. A., Khrapov S. S., Khoperskov A. V., “The Problem of Boundary Conditions for the Shallow Water Equations”, The Bulletin of Udmurt University. Mathematics. Mechanics. Computer Science, 26:3 (2016), 401–417 (in Russian) | DOI | MR | Zbl