scholarly journals The process of distribution Computer modeling of hazardous substances in the atmosphere taking into account the terrain relief

2021 ◽  
Vol 264 ◽  
pp. 01037
Author(s):  
Daler Sharipov ◽  
Zafar Abdullaev ◽  
Otabek Khafizov
Keyword(s):  
Mathematical Model ◽  
Climatic Factors ◽  
Software Tool ◽  
Hazardous Substances ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Factors Affecting ◽  
Transport And Diffusion ◽  
Harmful Substances ◽  
And Diffusion

The paper considers a mathematical model for research, forecasting, and management decisions on the process of spreading harmful aerosol substances in the atmosphere. When deriving a mathematical model of the object, the main weather and climatic factors affecting the process of transport and diffusion of harmful substances and the terrain of the region under consideration are taken into account. Changes in wind direction and speed are calculated using the Navier-Stokes equation of stream function and vortex velocity variables. The proposed software was implemented as a software tool in the Borland C ++ Builder environment to carry out computational experiments. The results of the performed numerical calculations are shown in the form of graphical objects.

scholarly journals Numerical Study Process Distribution of Contaminated Substances in the Atmosphere Taking Into Account the Physical and Mechanical Properties of Particles

2021 ◽  
pp. 10-15
Keyword(s):  
Numerical Study ◽  
Physical And Mechanical Properties ◽  
Software Tool ◽  
Industrial Emissions ◽  
Factors Affecting ◽  
Implicit Finite Difference Scheme ◽  
Implicit Finite Difference ◽  
Harmful Substances ◽  
Study Process ◽  
And Diffusion

The article deals with the numerical modeling of the processes of transfer and diffusion of air pollutants in the boundary layer of the atmosphere. A mathematical model of the spread of industrial emissions in the atmosphere was developed, taking into account the motion velocity of finely dispersed substances and a number of other factors affecting the change in the concentration of harmful substances in the atmosphere. The model is described by multidimensional partial differential equations with corresponding initial and boundary conditions. For the numerical integration of the problem, the method of splitting into physical processes (of transfer, diffusion and absorption) and an implicit finite-difference scheme of the second order of approximation in spatial variables and in time were used. A software tool was developed to conduct a computational experiment on a computer and to perform a comprehensive study of the processes of transfer and diffusion of harmful substances in the atmosphere

scholarly journals Computer Modeling of Aerosol Emissions Spread in the Atmosphere

2019 ◽  
Vol 97 ◽  
pp. 05023 ◽  
Author(s):  
Daler Sharipov ◽  
Sharofiddin Aynakulov ◽  
Otabek Khafizov
Keyword(s):  
Boundary Layer ◽  
Mathematical Model ◽  
Atmospheric Boundary Layer ◽  
Computer Modeling ◽  
Numerical Experiments ◽  
Climatic Factors ◽  
Numerical Algorithms ◽  
Aerosol Emissions ◽  
The Given ◽  
And Diffusion

The paper deals with the development of mathematical model and numerical algorithms for solving the problem of transfer and diffusion of aerosol emissions in the atmospheric boundary layer. The model takes into account several significant parameters such as terrain relief, characteristics of underlying surface and weather-climatic factors. A series of numerical experiments were conducted based on the given model. The obtained results presented here show how these factors affect aerosol emissions spread in the atmosphere.

scholarly journals About general solutions of Euler’s and Navier-Stokes equations

2019 ◽  
pp. 190-193
Author(s):  
V. I. Rozumniuk
Keyword(s):  
General Solution ◽  
Stokes Equation ◽  
Stokes Equations ◽  
Fundamental Problem ◽  
Diffusion Equations ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
General Solutions ◽  
And Diffusion

Constructing a general solution to the Navier-Stokes equation is a fundamental problem of current fluid mechanics and mathematics due to nonlinearity occurring when moving to Euler’s variables. A new transition procedure is proposed without appearing nonlinear terms in the equation, which makes it possible constructing a general solution to the Navier-Stokes equation as a combination of general solutions to Laplace’s and diffusion equations. Existence, uniqueness, and smoothness of the solutions to Euler's and Navier-Stokes equations are found out with investigating solutions to the Laplace and diffusion equations well-studied.

scholarly journals Method for predicting the dissemination of hazardous substances in the soil during long-term storage of galvanic waste

2022 ◽  
pp. 12-22
Author(s):  
Larisa Tretiakova ◽  
Liudmyla Mitiuk ◽  
Igor Panasiuk ◽  
Elina Rebuel
Keyword(s):  
Heavy Metals ◽  
Mathematical Model ◽  
Soil Salinity ◽  
Molecular Diffusion ◽  
Hazardous Substances ◽  
Depth Of Penetration ◽  
Long Term Storage ◽  
Harmful Substances ◽  
Term Storage

The problem of production waste storage in open areas of an enterprise with a galvanic shop for the production of chips and microchips has been investigated. The composition of the sludge obtained after sewage treatment of the production of the copper line was investigated. The aim of the article is to develop a mathematical model for predicting the distribution of compounds with heavy metals in the soil during long-term storage of galvanic sludge in open areas. Modeling the process of movement of salts from the earth's surface into the lower layers of the aeration zone occurs according to the laws of molecular diffusion. The method is developed on the basis of a mathematical model that makes it possible to estimate the spread over the depth of the ground and level of soil salinity over time using initial information about soil structure and its characteristics (molecular diffusion coefficient, volume humidity), annual volumes and conditions of sludge storage in the enterprise. Restrictions are set: the presence of harmful substances on the soil surface with a concentration that exceeds the permissible level; inadmissibility of harmful substances to aquifers. The practical use of the method made it possible to identify the main dangers during long-term storage of galvanic waste in open areas. The dynamics of soil salinity levels and the depth of penetration of heavy metals increase over twenty years of conservation has been determined, as well as the possibility of hazardous compounds entering groundwater has been assessed. Polyvinyl chloride packaging has a maximum life span of 15 years. Waste should not be stored in packages and in closed areas for more than 10 years. According to the prediction results, it can be stated that storage in landfills of galvanic waste for more than 15 years leads to significant salinization of the soil and creates conditions for an emergency situation, which is caused by harmful substances entering the water horizons. Recommendations for improving storage conditions are given and the need for recycling of industrial waste is substantiated

scholarly journals Visual analysis of flow and diffusion of hemolytic agents and hematomas

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Yafei Zhu ◽  
Mengyao Bao ◽  
Miaomiao Jiang ◽  
Jincai Chang ◽  
Jianzhong Cui
Keyword(s):  
Visual Analysis ◽  
Diffusion Theory ◽  
Medical Engineering ◽  
Initial Boundary ◽  
Drainage Tube ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Intracranial Hematomas ◽  
Control Equation ◽  
And Diffusion

AbstractThe elimination of intracranial hematomas has received widespread attention and the interactions between hemolytic agents and hematomas have become a hot research topic. In this study, we used the Navier-Stokes equation to describe the flow control equation for hemolytic agents in a tube and used Fick’s law and the Maxwell-Stefan diffusion theory to describe the diffusion and mass transfer of hemolytic agents and hematomas. The physical fields and initial boundary conditions were set according to the parametric properties of the fluid and drainage tube. The COMSOL Multiphysics software was used to simulate the streamline distribution of hemolytic agents in a bifurcated drainage tube. Additionally, the diffusion behaviors of the hemolytic agents into hematomas were simulated and visual analysis of coupled multiphysics was performed to realize the digitization and visualization of engineering fluid problems and contribute to the field of medical engineering.

scholarly journals Increasing the efficiency of highly concentrated coal-water fuel based on the simulation of non-Newtonian fluid flow

2019 ◽  
Vol 294 ◽  
pp. 01009 ◽  
Author(s):  
Nataliya Chernetskaya-Beletskaya ◽  
Andriy Rogovyi ◽  
Igor Baranov ◽  
Alexander Krut ◽  
Maria Miroshnikova ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Energy Consumption ◽  
Transport System ◽  
Three Dimensional ◽  
Transport Systems ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Industrial Enterprises ◽  
Energy Consumption Optimization ◽  
The Mathematical Model

The analysis of further prospects for increasing the efficiency of transportation of coal-water fuel in hydro-transport systems of industrial enterprises is carried out. The mathematical model of the spatial three-dimensional flow of coal-water fuel was developed on the basis of SST turbulence model based on the solution of Navier-Stokes equation. As a result of the calculation, the values of pressure loss, flow rate and velocity distribution over the cross section of the pipeline in the straight section and in the turn were determined, which allowed determining the energy consumption during coal-water fuel transportation in the industrial hydro-transport system. The performed studies allowed us to refine the mathematical model of water-coal suspension flow and, thus, improve the patterns of influence of hydro-transportation scheme and parameters of coal-water fuel on energy consumption for its supply to enterprise consumers. By means of mathematical model of non-Newtonian fluids flow, the patterns of influence of hydro-transport system parameters and transportation modes of coal-water fuel on its energy indicators in industrial hydro-transport systems are determined. The obtained results are related to reduction of energy consumption, optimization of enterprise transport network configuration and increase of efficiency of coal-water fuel transportation to enterprise energy facilities.

Mathematical Model of Nanostructure Formation in Binary Alloys at Electron Beam Treatment

2016 ◽  
Vol 870 ◽  
pp. 34-39 ◽  
Author(s):  
Sergey A. Nevskii ◽  
Vladimir D. Sarychev ◽  
Sergey V. Konovalov ◽  
D. Kosinov ◽  
Irina Komissarova
Keyword(s):  
Mathematical Model ◽  
Electron Beam ◽  
Binary Alloys ◽  
Navier Stokes ◽  
Concentration Gradients ◽  
Surface Layers ◽  
Depth Of Penetration ◽  
Navier Stokes Equation ◽  
Critical Wavelength ◽  
Current Electron

The paper presents a thermoconcentration and capillary mathematical model, describing the formation of 10 to 100 nm structures in the surface layers of binary alloys irradiated by low-energy, high-current electron beams of submillisecond duration. The model is studied by the example of “ferrum - carbon” and “titanium – carbon” systems. It comprises Navier-Stokes equation, thermoconductivity and diffusion equations, as well as surface kinematic and dynamic boundary conditions. The effect of electron beam on material is specified as various temperature and concentration gradients. A dispersion equation for thermocapillary waves in nanowavelength range is developed and analyzed with thin layer approximation. The critical wavelength, leading to this instability, is revealed. It is found out that its values are 17.39 nm for Fe-С and 69.7 nm for Ti-C at the depth of penetration ~ 10-5 m. Wavelengths are compared to the dimensions of crystallization cells and structures, which are formed in them. The paper shows that the model provides a rational explanation of registered regularities.

scholarly journals The Stokes complex for Virtual Elements in three dimensions

2020 ◽  
Vol 30 (03) ◽  
pp. 477-512 ◽  
Author(s):  
L. Beirão da Veiga ◽  
F. Dassi ◽  
G. Vacca
Keyword(s):  
Complex Structure ◽  
Natural Extension ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Main Motivation ◽  
Divergence Free ◽  
Discrete Spaces ◽  
Vector Valued ◽  
And Diffusion

This paper has two objectives. On one side, we develop and test numerically divergence-free Virtual Elements in three dimensions, for variable “polynomial” order. These are the natural extension of the two-dimensional divergence-free VEM elements, with some modification that allows for a better computational efficiency. We test the element’s performance both for the Stokes and (diffusion dominated) Navier–Stokes equation. The second, and perhaps main, motivation is to show that our scheme, also in three dimensions, enjoys an underlying discrete Stokes complex structure. We build a pair of virtual discrete spaces based on general polytopal partitions, the first one being scalar and the second one being vector valued, such that when coupled with our velocity and pressure spaces, yield a discrete Stokes complex.

Mathematical modeling of electron irradiation of oil

2018 ◽  
Vol 35 (5) ◽  
pp. 1998-2009
Author(s):  
Assylzhan Kizbayev ◽  
Dauren Zhakebayev ◽  
Ualikhan Abdibekov ◽  
Askar Khikmetov
Keyword(s):  
Mathematical Model ◽  
Electron Irradiation ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Hydrocarbon Mixture ◽  
Navier Stokes Equation ◽  
Content Type ◽  
The Matrix ◽  
Crank Nicolson

Purpose This paper aims to propose a mathematical model and numerical modeling to study the behavior of low conductive incompressible multicomponent hydrocarbon mixture in a channel under the influence of electron irradiation. In addition, it also aims to present additional mechanisms to study the radiation transfer and the separation of the mixture’s components. Design/methodology/approach The three-dimensional non-stationary Navier–Stokes equation is the basis for this model. The Adams–Bashforth scheme is used to solve the convective terms of the equation of motion using a fourth-order accuracy five-point elimination method, and the viscous terms are computed with the Crank–Nicolson method. The Poisson equation is solved with the matrix sweep method and the concentration and electron irradiation equations are solved with the Crank–Nicolson method too. Findings It shows high computational efficiency and good estimation quality. On the basis of numerical results of mathematical model, the effect of the separation of mixture to fractions with various physical characteristics was obtained. The obtained results contribute to the improvement of technologies for obtaining high-quality oil products through oil separation into light and heavy fractions. Mathematical model is approbated based on test problem, and has good agreement with the experimental data. Originality/value The constructed mathematical model makes developing a methodology for conducting experimental studies of this phenomenon possible.

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