Research On Pollutant Migration Based On Random Diffusion Process

In order to reveal the time-space evolution of water quality, and analyse the waterquality evolution and distribution of the contaminated zone when the sewage runs into thewater,and avoid multi-lake connection and cross-contamination in the rivers and lakes, thispaper analyszes the water diffusion theory of pollutants, and the pollution concentrationtrends and the internal law of water movement in details, which is on the basis of the basicprinciples of stochastic processes, combing with pollutant concentration diffusion ohmtheorem and geometric Brownian motion, and establish a water quality mathematicalmodel about the migration of point source and non-point source water which cancalculate the average pollution concentration of the dye groups, and gets the longaxis, short axis, area formulas of the contamination.Fick’s law describes the relation between diffusion flow and diffusion of thesubstance concentration gradient in the diffusion system. By analyzing the transformationmechanism of pollutants in the body of water movement, we get a further understandingof Fick’s law, then the law of pollutants transforming in the water body is gained. In therelevant theory of stochastic processes, Brownian motion, geometric Brownian motion,we use the random walk approximation of the continuous model to prove that theproliferation of pollutant concentrations comply with the geometric Brownian motion,furthermore, research the transferring probability density function with Kolmogorovequation in Brownian motion and Ornstein-Uhlenbeck process. These prove thetheoretical bases for the water transport model.The paper analyzes the migration process of the pollutants in the water column indetails, establishes water migration coordinate system, and analyzes the diffusion theoryand pollution in horizontal, vertical and plumb directions, and describes the viscosity ofinfluencing the dispersion of pollutants coefficient, attenuation coefficient, watermigration coefficient. This is the realistic basis of water quality transport models.Sub-instantaneous point source model and Sub-instantaneous non-point sourcemodel, the two types of models describe the length, width and area of contaminated zoneon the two-dimensional plane, and give the mathematical variance expression of theexpectations and the calculation; the paper use random formulas and random processtheory to solve the model. We test the parameter calibration and model with an instance.