A computer simulation of the Volga River hydrological regime: a problem of water-retaining dam optimal location.

We investigate of a special dam optimal location at the Volga river in 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 the spring flooding due to the overregulation of the Lower Volga. By using a numerical integration of Saint-Vacant equations we study the water dynamics across the northern part of the Volga-Akhtuba floodplain with 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 provide us the dam coordinated with the maximum value of ${V_A}$. Such approach to the dam location choice let us to find the best solution, that the value $V_A$ increases by a factor of 2. Our analysis demonstrate a good potential of the numerical simulations in the field of hydraulic works.