The Research Of The Numerical Theory And Method For The Navier-Stokes Equations

The Navier-Stokes equations that can be used to describe the complexity and variety of fluid dynamical phenomena.Through the numerical simulation of Navier Stokes equations,we can study the dynamic phenomena such as turbulence,vortex,etc.In this paper,a novel linear second-order stable numerical method for solving the stream function-vorticity form of nonstationary Navier-Stokes equations at high Reynolds number is presented.We implement the second-order linear scheme by combining the finite difference method(FDM)and finite volume method(FVM),on a staggered-mesh grid system,which typically consists of two steps:prediction and correction.Furthermore,we show in a rigorous fashion that the scheme is stable and uniquely solvable.On the basis of rigorous proof about this theory,a verification algorithm that has the analytical solution is designed to demonstrate the effectiveness of our scheme via the errors and the order of convergence testing in L~2-and L~?-norm.Furthermore,Numerical experiments are performed for solving the nonstationary Navier-Stokes equations in the vortical flow of two-dimensional vortex merging at different high Reynolds numbers.The merging process of a pair of(or more)co-rotating vortices are numerically simulated,and the effects of different parameters on the merging process are analyzed.