Numerical Simulation of Three-Dimensional Unsteady Viscous Flow Using Higher Order Accurate Difference Method

Abstract

A new direct simulation scheme using the eighth order accurate difference method is presented for three-dimensional instability of plane Poiseuille flow. The vorticity transport equation is transformed into a set of ordinary differential equations in time by using modified differential quadra-ture (MDQ) method for spatial discretization. The time integration is carried out by Runge-Kutta-Gill (RKG) scheme. The Poisson equations with respect to the vector potential are also discretized by MDQ method and solved by the iteration method. The multiple grid method, in addition, is employed to accelerate its convergence. The present method is compared with other method based on the primitive variables for certification. And further, our results of the amplitude decay and oscillation frequency of the disturbance, agree with those of pseudo-spectral method by Orszag, and the accuracy and efficiency of the present method is shown.