The Spatial Iterative Method For The Incompressible Navier-Stokes Equations And Their Coupled Problems

The Navier-Stokes equations of incompressible flow are widely used in science and engineering.It is a motion equation describing momentum conservation of viscous incompressible fluid and reflects the basic mechanical law of viscous fluid flow,which is of great significance in fluid mechanics research.However,due to the nonlinearity of Navier-Stokes equations of incompressible flow.It is difficult to make theoretical analysis and numerical calculation.Therefore,efficient and stable algorithm research is still our focus.Convection diffusion phenomena include river pollution,air pollution,pollutant distribution in nuclear waste pollution,fluid flow and heat conduction in fluid.The theory of double diffusion convection is a branch of hydrodynamics developed by oceanographers and hydromechanics in recent years.It mainly investigates the hydrodynamic stability and convection patterns with two diffusion mechanisms(such as thermal diffusion and solute diffusion).On the basis of previous studies,this paper studies the suitability and effectiveness of the spatiotemporal iteration method from the theoretical and numerical perspectives based on the spatiotemporal iteration solution scheme of the low-order nonconforming finite element.The convergence rate,computational efficiency and algorithm complexity of the three iterative methods are compared.In this paper,the nonconforming finite element method is used because it is compared with the conforming finite element method.Incompressible flow of nonconforming finite element method due to its simplicity and smaller basis function support set is more popular in recent years.In addition,they are more likely to satisfy the discrete information support conditions.The nonconforming finite element can easily relax conforming finite element higher-order continuity requirements.Therefore,in practice,the nonconforming finite element method seems to be superior to conforming finite element method.This paper is mainly divided into two parts.?.Based on the low-order nonconforming finite element pair,the simple iterative scheme,Oseen iterative scheme,and Newton iterative scheme are used to solve the Navier-Stokes equation of the incompressible flow.From a theoretical perspective,the stability and convergence of the three iterative schemes are discussed.From the numerical point of view,the two sides of convergence speed and convergence rate are compared under different viscosity conditions.The results show that the three iterative schemes all have the optimal order of convergence.In the case of large viscosity,the Newton iterative scheme converges fastest.In the case of small stickiness,only the Oseen iteration scheme can solve the stationary Navier-Stokes problem.?.Based on the low-order nonconforming finite element pair,the simple iterative scheme,Oseen iterative scheme and Newton iterative scheme were respectively used to solve the steady double diffusion convection equations.From a theoretical perspective,the stability and convergence of the three iterative schemes are discussed.In numerical calculations,three different iterative formats are used for Navier-Stokes in the equations,while the temperature and concentration equations are not solved iteratively.The final numerical results confirm the effectiveness of the algorithm.The Newton iteration format is more efficient than the other two iteration formats,which can save CPU time.In the two numerical experiments in this paper,the iterative method of the nonconforming finite element is effective.In addition,it is not difficult to find from the numerical simulation that the Oseen iteration format is always better under the condition of small viscosity coefficient.In the case of large viscosity coefficient,Newton iteration scheme is complex,but the computation time is shorter.The three iterative methods have their own advantages.If a small viscosity coefficient is selected in the experiment,Oseen iteration will be given priority.When the viscosity coefficient is large,the efficient Newton iteration scheme can be considered.