Abstract
Efficient direct simulation methods for instability of parallel flows as well as non-parallel flow are proposed. The computational method consists of the 4-th order accurate modified differential quadrature method for spatial discretization, Runge-Kutta-Gill time integration scheme and the new direct Poisson solver with 4-th order accuracy. The present methods are at first applied to direct simulation on instability of plane and Hagen Poiseuille flows, which are parallel flows, and it is shown that the temporal evolution of the perturbation superposed on the basic flows is simulated accurately on comparison with pseudo-spectral and Chebyshev polynomial expansion method. Next this method is applied to the direct simulation of spatial instability of boundary layer, which is non-parallel flow, and its efficiency is confirmed.
