The results of the numerical simulations of the dynamics of shallow waters for Volga-Akhtuba Floodplain are discussed. The mathematical model is based on the system of Saint-Venant equations. Numerical solution applies a combined LagrangianEulerian (cSPH-TVD) algorithm. We have investigated the features of the spring flood in 2011 and found the inapplicability of the hydrodynamical model with the constant roughness coefficient . We have found a good agreement between the results of numerical simulations and the observational data at gauging stations which allows us to estimate in low water min = 0.02 and the maximum water level in the river Volga max = 0.06-0.07.

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 VolgaAkhtuba oodplain related to insucient water amount during spring oodings 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 oodplain 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 ow through the Volga Hydroelectric Power Station (so-called hydrograph which characterises the water ow per unit of time). By varying the location of the water-retaining damas well as various ow spatial structure on the territory during the ood period. Gradient descent method provides the dam coordinated with the maximum value of V A . Such approach to the dam location choice let us nd 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 eld of hydraulic works.

A mathematical model of the joint dynamics of shallow waters, entrained and suspended sediments is constructed, which takes into account nonlinear fluid dynamics and bottom deformations. The dynamics of shallow waters is described by the Saint-Venant equations taking into account the spatially inhomogeneous distribution of the terrain. The transport of entrained sediments is described by the Exner equation generalized to the case of an inhomogeneous distribution of the parameters of the underlying surface. The dynamics of suspended sediments is described by the transport equation, which includes convective transport by water flow and the process of diffusion of the suspension in the liquid layer. For numerical integration of the Saint-Venant, Exner equations and suspended sediment dynamics, a stable and well-tested CSPH-TVD method of the second order of accuracy is used, the parallel CUDA algorithm of which is implemented in the form of a software package «EcoGIS-Simulation» for highperformance computing on supercomputers with graphics coprocessors (GPU). The conditions for the development of a quarry of non-metallic building materials (NSM) located at the mouth of the Partridge Volozhka of the Volga-Akhtuba floodplain on the 2549–2550 km section of the Volga River are considered. To study the safety of navigation from the lower reaches of the Volga hydroelectric dam to the entrance to the VDSK, numerical hydrodynamic modeling of the dynamics of channel processes in this section of the Volga River was carried out. Based on the results of mathematical modeling of the joint dynamics of surface waters, entrained and suspended sediments in the riverbed of the Volga River, it is concluded that the development of the NSM quarry considered in the work does not significantly affect the safety of navigation both along the main ship course «The lower reaches of the Volga hydroelectric dam — VDSK» and on additional — «Volgograd zaton» and «Volozhka Partridge».

We consider the possibilities of numerical hydrodynamic modeling for the construction of cadastral maps of dangerous flood zones on the example of the Volgograd region. The numerical model is based on shallow water equations and Combined Smooth Particle Hydrodynamics-Total Variation Diminishing (CSPH-TVD) method for integrating hyperbolic differential equations. To create a digital elevation model (DEM), we use an iterative approach, assimilating all available spatial data, including remote sensing data, topographic measurements and observations of flooding in different years. The agreement of the observed data with the numerical simulation results can significantly improve the quality of the DEM. Digital elevation models are based on elevation matrices in increments of 3 to 10 meters, depending on the topography of the study area. The result of our work is a set of maps with flood boundaries for different probabilities of catastrophic events. For each such flood, we calculate the river hydrograph and its integral characteristics.

The problem of flooding of territories with flood waters for settlements of the Volgograd region is considered. A numerical model of flood water dynamics is constructed, taking into account the topography of the terrain. The simulation is based on two-dimensional shallow water equations. For computational experiments, a parallel implementation of the numerical scheme CSPH-TVD for NVIDIA graphics accelerators with CUDA technology is used. The digital model of the river-bed and floodplain relief is based on spatial data SRTM3 and SRTMGL, topographic maps of the area, longitudinal profiles of rivers. The water flow rates for the Buzuluk and Perevozinka rivers are determined and a hydrograph of the Volga hydroelectric power station is constructed for the given probabilities of exceeding the water level. Flood maps were obtained for the following localities: Novoannisky, Berezovka 1st, kh. Vyazovka. The maximum values of the depths for 1 %, 3 %, 5 %, 10 %, 25 % and 50 % of water security are presented. An analysis of the flood situation was carried out and appropriate engineering and protective measures for settlements were proposed. At maximum flood water levels, residential buildings of kh. Berezovka 1-I are not subject to flooding. In order to minimize the negative impact for the city of Novoanninsky, it is proposed to carry out timely clearing of the river-bed of the Perevozinka river from congestion. To protect from flooding ch. Vyazovka it is recommended to use diversion dyke.