Numerical Methods For The Coupled Navier-Stokes/Navier-Stokes Equations

The coupled Navier-Stokes/Navier-Stokes equations are the multi-physical coupling model in computational fluid dynamics.They describe complex natural phenomena and fluid motion,mainly appear in theoretical studies such as meteorology and oceanography.Compared with the single physical model,the multi-physics coupled model can better describe the physical process of natural phenomena.By understanding and analyzing models,we can better grasp the nature of many natural phenomena.However,because the coupled Navier-Stokes/Navier-Stokes equations have strong coupling and nonlinear properties,it is difficult to find the exact solution of the equations.Therefore,it is extremely important to construct a stable and efficient numerical algorithm to solve the coupled Navier-Stokes/Navier-Stokes equations.Because of the large storage space and long calculation time required in the numerical simulation of the coupled Navier-Stokes/Navier-Stokes equations,in order to improve the calculation efficiency and reduce the storage resources,this paper mainly works on the coupled Navier-Stokes/Navier-Stokes equations as follows based on the previous work:First,the local and parallel decoupled time stepping of spatial non-iterative Oseen scheme is given.Based on the Euler space-time method of spatial non-iterative Oseen scheme,combined with the domain decomposition technique of the unity partition,the coupled Navier-Stokes/Navier-Stokes equations were transformed into the nonstationary Navier-Stokes equations which is using Oseen scheme for one-step linear correction in the space and advancing step by step in time.At the same time,the domain decomposition basis function is introduced in the process of solving in the local parallel domains.Finally,the numerical solutions of the coupled Navier-Stokes/Navier-Stokes equations are obtained by accumulating the numerical solutions of the local parallel domains.The numerical results show that compared with the Euler time method of spatial non-iterative Oseen scheme,the local and parallel decoupled time stepping method converges faster,which improves the computational efficiency of the coupled equations.Second,the local and parallel decoupled time stepping and the Euler space-time method of spatial non-iterative Newton scheme are given.According to the Newton iterative scheme,based on the Euler time method of spatial non-iterative Oseen scheme,the Euler time method of spatial non-iterative Newton scheme is linearly corrected by the non-iterative Newton scheme in the nonlinear term,the coupling terms are bounded by the geometric averaging of the jump.Combined with the domain decomposition techniques of unity partition,the local and parallel decoupled time stepping of spatial non-iterative Newton scheme is proposed to transform large-scale serial problems into small-scale parallel problems and the longest computation time of the local parallel domains is used as the parallel time at the same time.By solving the numerical solution of the local parallel domain,the domain decomposition basis function is introduced and the numerical solution of the coupled Navier-Stokes/Navier-Stokes equations are obtained by using the superposition principle and linear combination.The numerical results show that compared with Newton iterative scheme,Oseen iterative scheme and simple iterative scheme,the Euler time method of spatial non-iterative Newton scheme has higher error accuracy and shorter calculation time.The time-decoupled local parallel method of spatial non-iterative Newton format has shorter calculation time and is more efficient.The local and parallel decoupled time stepping method of spatial non-iterative Newton scheme has shorter calculation time and is more efficient.