Efficient Iterative Methods For The Incompressible Coupled Navier-stokes Equations

In this thesis,the effcient iterative algorithms are constructed for the incompressible Navier–Stokes equations and temperature equations(or Maxwell’s equations).First,a new highly efficient iterative method based on classical Oseen iteration is presented to solve the natural convection equations,which we compute a nonlinear system based on classical Oseen iteration method,then use the error correction strategy to control the error arising and to solve a linear system.The new iterative method not only retains the advantage of the Oseen scheme,but also saves computational time and iterative step for solving the considered problem.The stability analysis and iterative error estimates are deduced.Next,based on the basic idea of two level method,we construct a efficient two-level algorithm for solving the stationary incompressible Magnetohydrodynamics(MHD)equations.This algorithm is consisting of solving one nonlinear system on a coarse mesh with mesh size H and two linearized problems with different loads on a fine mesh with mesh size h.Compared with existing work on the two-level method for the MHD model,our two-level method allows a much high order scaling between the coarse and fine grid sizes.Besides,the stability analysis and error estimate of the algorithm are presented,the efficiency of the algorithm is indicated by the numerical results.