This article is cited in 2 papers

MATHEMATICAL MODELING

Numerical simulation of impurity transport in continuous medium using supercomputer modeling

E. V. Baskakov

Volgograd Technical University, Volgograd, Russia

Abstract: The article describes modeling the spread of impurities in a continuous medium using the oil leak from a pipeline laid along the bottom of a reservoir as an example, based on the software developed using supercomputer technologies in the C language. A mathematical model is proposed that describes the process of impurity transport in the aquatic environment. The problem is reduced to solving a system of two equations: a generalized differential equation for the transfer of impurities and an equation for the velocity field. In the generalized equation for the transport of impurities, the variable from the function can be expressed by different parameters; within the framework of this problem, the variable is a concentration. In the simulated situation, oil products leak from the main pipeline, the oil products continuously flow into the water source. For the study, there was simulated the area with given boundaries and initial parameters: the size of the area, the flow velocity and the density of the medium. The process of developing and testing a software package based on OpenMP-CUDA is presented. The functionality of the created program allows you to predict the speed and range of propagation of various impurities in various environments with a visual representation. The software package consists of two modules: calculation and visualization. The calculation module is implemented by transferring the computational load to the video card. The graphics module is implemented in Python using the Matplotlib library. The results of numerical simulation of the propagation of a pollutant in a continuous medium are presented. The result obtained coincides with a coincidence with the real situation and the results of other studies. With increasing amount of experimental data and dependent variables (ambient temperature, water salinity, etc.), the accuracy of modeling will increase. The analysis of oil leakage at different fistulas was made in case of an accident and comparison with the results of computer simulation.

Keywords: impurity transport, software package, mathematical model, numerical simulation, pipeline, leak formula, OpenMP, CUDA, graphics accelerator, oil outflow.

UDC: 004.942

Received: 04.03.2023
Accepted: 10.07.2023

DOI: 10.24143/2072-9502-2023-3-97-104