Research On FADE Model Based On Solute Transport In Groundwater

Groundwater is closely related to our life.With the expansion of human activities,the pollution and damage to groundwater resources are becoming more and more serious.Therefore,water,as a necessary material in human life activities,is extremely urgent to control groundwater pollution and protect resources.With the gradual improvement of human attention to environmental problems,the related scholars are also deepening the research on the solute transport in groundwater,especially the numerical calculation methods are becoming more and more mature,and the groundwater simulation has made a breakthrough development.This paper is divided into six chapters.The first chapter summarizes the research significance and research status at home and abroad.In chapter 2,the definition and basic properties of diffusion equation,convection-dispersion equation,integral transformation,fractional derivative are introduced.Chapters 3 to 5 discuss three kinds of time fractional models based on solute transport in groundwater.Finally,the conclusion and prospect are given.In chapter 3,the fractional convection-dispersion model of moving/stationary is studied.By improving the traditional model,the fractional convection-dispersion equation is discussed,and the analytical expression is derived by Fourier transform and Laplace transform.The relationship between concentration and fractional order is described by calculating the value of its parameters and drawing the graph: the fractional convection-dispersion equation has "trailing" phenomenon,which is in line with the movement phenomenon of solute transport in groundwater.In chapter 4,the diffusion model of solute transport in groundwater based on Caputo time fractional derivative is discussed.Firstly,according to the mass conservation law of matter,a linear partial differential equation model is established,and the analytical expression of solute concentration can be obtained by using the undetermined coefficient method.The relationship between concentration and distance and time in the process of mass migration is discussed by numerical experiments.Chapter 5 considers the model of distributed order convection-dispersion equation.Firstly,according to the definition of distribution order,the distribution order term of the equation is discretized,and other terms of the model are discretized.The discretized results are sorted into a difference scheme,and the stability and convergence of the difference scheme are analyzed and proved.Finally,an example is given to solve the problem with MATLAB.