Two Finite Element Algorithms For Steady Natural Convection Heat Transfer Problem

The natural convection heat transfer problem describes the law of a kind of viscous incompressible fluid,which is an important problem in computational fluid mechanics.However,due to the coupling and non-linearity of the system itself,it is very difficult in numerical calculation and theoretical research.Therefore,in order to simplify these difficulties,it is very important to construct and study an efficient algorithm.Standard finite element method solution of the equation(such as the Galerkin method),usually involves three approximation space,but it is not can freely choose,should meet the inf-sup or LBB condition,it is a key to keep mixed finite element method success.At present,some literatures have discussed numerical methods of natural convection equations,but only a small number of stabilization methods make the finite element space not necessarily satisfy the LBB condition.In addition,according to the character of natural convection heat transfer problem itself,if do the numerical simulation directly,you need a lot of computing time.In view of these difficulties in natural convection heat transfer,this paper presents two algorithms,one is the streamline diffusion finite element method,which solves the limitation problem in selecting finite element space,so that you can choose any The finite element group pairing,the existence,uniqueness,stability and error estimation of the discrete solution are also proved.The other is two-level decoupling parallel correction method.This method not only improves the calculation efficiency,but also further studies the correlation between the error and parameters when the coarse grid and the fine grid meet the relational expression: (?).There are different Rayleigh Numbers Ra given in numerical experiments to verify the theoretical analysis,and the results show that the method is effective to solving the natural convection heat transfer equation.