A Decoupling Method For Coupled Navier-Stokes And Darcy Flows

In recent years, the problems of the coupling of free ?uid and prorous media ?ows have become one of the most important branches of the ?eld of computational ?uid mechanics and enormously promoted the development of industrial production and engineering ?eld, such as the petroleum engineering, the simulation of the water and soil pollution. The coupling problem usually contains two meanings which are the coupling between two ?uid ?elds and the coupling between ?ow equations and mass transfer equations. This dual coupling problems make the system extremely complicated. Therefore, it is an important research subject to seek an effective decoupling method.In this thesis, a decoupling method with diffierent subdomain time steps for the non-stationary Navier-Stokes/Darcy model is formulated and analyzed. The method has asynchronous time steps, which adopt small time steps in the ?uid region and adopt large time steps in the porous region. It saves a lot of CPU time. Stability and convergence of the method are proved. A serie of numerical results are presented to illustrate the features of the proposed method.In addition, to overcome the difficulties caused by discrete nonlinear term and nonphysical oscillation, we study a stabilized characteristic-nonconforming ?nite element method to solve the non-stationary incompressible Navier-Stokes equations. The characteristic scheme is used to deal with advection term and temporal differentiation,which avoid some difficulties caused by trilinear terms. The space discretization utilizes the nonconforming lowest equal-order pair of mixed ?nite elements(i.e.N CP1-P1).The stability analysis and optimal order error estimates for velocity and pressure are presented. Finally, we shown that using stabilized characteristic-nonconforming ?nite element method to solve Navier-Stokes problems is more stable and effective.