Two-level Defect-correction Methods For Incompressible Fluid With Nonlinear Slipboundary Conditions

Navier-Stokes equations are the important nonlinear equations, and have widely application in real life.Through the in-depth study of the model, it can help us to understand the laws of nature and provide a more effective method to nonlinear science theory and fluid mechanics application in the industry.Based on the defect-correction method, this master thesis mainly studies the two-level finite element methods for Navier-Stokes variational inequality problems at large Reynolds number.The thesis is arranged as follows:The first chapter introduces the physical background and current research situation of Navier-Stokes variational inequality problems and the studies of the main problems and methods in this article;The second chapter outlines some knowledge of the reserves and the existence and uniqueness solution of the Navier- Stokes equations,study the questions of the unsteady Navier-Stokes variation inequality problemsunder the two-lever defect-correction methods,then the numerical experiment is given to verify the result in theory;The third chapter research the variational problem of Smagorinsky type by two-level defect-correction method under the system of LES,we get its error estimation of true solution and approximation solution.Finally, numerical experiments are given to verify the accuracy of the results;The fourth chapter is summaries and prospect.