Fourier Analysis Method for Numerical Solution of Navier-Stokes Equations

摘要

Solutions of the initial-value problem of non-stationary Navier-Stokes equations for the flow of viscous incom pressible fluids with given initial conditions are obtained. The flow is assumed to be periodic in space-variables in the entire space. The solution is first expressed in Fourier series whose coefficients (which are functions of time) are then obtained from a set of simultaneous ordinary differential equations by numerical methods. Different initial conditions for both two and three dimensional problems are considered. Results showing the behaviour of some of the Fourier coefficients with time, as well as the space-averages of kinetic energy and vorticity, are given for three different problems. (Author)