Alexander Sukhinov

3D Model of pollution distribution in city air and its parallel realization

The monitoring of atmospheric air pollution in urban conditions is large-scale problem. It is necessary to take into account many environmental parameters. As a result numerical algorithms are complicated and need many system resources. It was decided to use object—oriented technologies in association with parallel development methods to provide operative estimation of environmental conditions.

Three-Dimensional Mathematical Model of Wave Propagation Towards the Shore

To describe wave processes, we use here a system of Navier–Stokes equations containing three equations of motion in regions with dynamically varying geometry of the computational domain. The pressure correction method was used to approximate the hydrodynamic model difference schemes that describe the mathematical model of wave propagation towards the shore. This model was constructed on the basis of an integro-interpolation method using a scheme with weights. An adaptive alternating-triangular iterative method was used to solve the system of equations. The practical significance of the numerical algorithms and the complex of programs implementing them is determined by the possibility of application in the study of hydrophysical processes in coastal water systems, as well as in the construction of the velocity and pressure fields of the aquatic environment. They also make it possible to assess the hydrodynamic effect on shore protection structures and coastal structures in the presence of surface waves.

Parallel Solution of Sediment and Suspension Transportation Problems on the Basis of Explicit Schemes

The article has been devoted to construction and investigation of parallel algorithms for the numerical realization of 3D models of suspended matter transportation and deposition and 2D models of bottom sediment transportation in sea coastal systems on the basis of explicit schemes with regularization terms that provide improved stability quality. The developed models take into account coastal currents and stress near the bottom caused by wind waves, turbulent spatial-three-dimensional motion of the water medium, particle size distribution and porosity of bottom sediments and hydraulic size of suspended particles, complicated shoreline shape and bottom relief and other factors. The numerical realization of the suspension transportation problem is carried out on the basis of explicit regularized difference schemes. The discrete model is constructed by means of including additional term according to idea of B. Chetverushkin – a discrete analogue of a second-order difference derivative with a small factor has been inserted in right side diffusion-advection equation. The value of the small factor determined on the basis of physical considerations and stability conditions. Compared with traditional parallel algorithms oriented to the use of implicit schemes, the use of explicit regularized algorithms allows to reduce the time of numerical solution of problems on a multi-core computing system with distributed memory containing 2048 cores and a peak performance of 18 Tflops in 12–80 times. The program package constructed by the authors for parallel realization given models has practical significance: it will allow to improve the accuracy of the real-time forecast and the validity of the engineering solutions taken for coastal infrastructure projects.

Supercomputer Modeling of Hydrochemical Condition of Shallow Waters in Summer Taking into Account the Influence of the Environment

The paper deals with the development and research of a mathematical model for hydrophysical processes which involves the use of modern information technologies and computational methods with the aim to improve the accuracy of predictive modeling of ecological condition of shallow waters during the summer. The model takes into account the following factors: movement of water flows; microturbulent diffusion; gravitational settling of pollutants; nonlinear interaction of plankton populations; nutrient, temperature and oxygen regimes; and impact of salinity. A scheme with weights is proposed for the discretization of the proposed model. This scheme significantly reduces both error and computation time. The practical significance of the paper is determined by the software implementation of the model and the determination of the limits and prospects of its practical use. Experimental software is designed on the basis of a supercomputer for mathematical modeling of possible development scenarios of shallow water ecosystems taking into account the influence of the environment. For this, we consider as an example the Sea of Azov in the summer period. The software parallel implementation involves decomposition methods for computationally intensive diffusion-convection problems taking account of the architecture and parameters of a multiprocessor computer system. The software complex contains a model for fluid dynamics which includes equations of motion in three coordinate directions.