Theoretical Analysis And Numerical Simulation Of Coupled Mathematical Model Of The Karst Aquifer

In this dissertation, the fluid flow in the karst aquifer is extensively studied.In the first chapter, we introduce the basic conception of karst aquifer and the related mathematical models.We then, in the second chapter, investigate two types of models that possess the most famous celebrity, namely the Stokes-Brinkman system and the Stokes-Darcy sys-tem. To compare these models, we introduce a non-dimensional number, which is defined as the square root of the permeability divided by the square root of porosity and then divided by the typical length scale. With this non-dimensional number, we adopt the asymptotic expansion of the Stokes-Darcy system with respect to four dif-ferent interface conditions, comparing which with the solutions of Stokes-Brinkman system. Our results imply that in both one-dimensional and two-dimensional case, in the conduit the solution of the Stokes-Darcy system with the Beavers-Joseph interface condition fits better than does the solution obtained using the Beavers-Joseph-Saffman-Jones interface condition and both are better than the solutions obtained using the zero tangential velocity interface condition, and the free-slip interface boundary condition is the worst among the four. On the other hand, the difference between the velocity in the porous media for the Stokes-Brinkman system and the Stokes-Darcy equations with all the interface conditions are the same.In the third chapter, we study the coupled continuum pipe-flow (CCPF) model, which is now widely utilized in the real-world topics. The most interesting issue in CCPF model is how to select the unknown exchange rate. To this end, we select the Stokes-Darcy system as the "true" model and compare the relative error between CCPF model and Stokes-Darcy system by choosing four different kinds of criterion. We cali-brate the exchange rate by decreasing the difference between the two models. Besides proposing the approximate exchange rate, we also study the sensitivity of the solution with the variation of the exchange rate as well as the parameters.