Research On Uzawa Iterative Method For The Natural Convection Problem

In this paper,the numerical solution of steady natural convection model is discussed,and the Uzawa algorithm is constructed based on the theoretical analysis and framework of classical finite element method.Firstly,the Uzawa algorithm based on mixed finite element is used to deal with the natural convection model.The nonlinear term is processed by Ossen iterative format,and the pressure is iterated separately,and the velocity is calculated by decoupling.In this paper,the corresponding stability analysis,error estimation,numerical examples and experimental results are presented the Uzawa algorithm is effective.Secondly,when the Uzawa method is used to calculate the natural convection model,it is found that the relaxation parameter has a great influence on the solution.In order to explore the influence of the perturbation of the relaxation parameter on the solution,the sensitivity equation is used for the analysis.The main idea of this algorithm is to Uzawa square of the steady natural convection model.A new system of linear partial differential equations is obtained by differentiating the relaxation parameters.The stability analysis and numerical experiments are carried out.The experimental results show that the proposed algorithm is better than the standard coupling algorithm save computation time.Therefore,the Uzawa method is worth exploring to solve the natural convection model.