Abstract
Abstract A new eighth-order accurate method is presented for simulating directly turbulent shear flows. In the present method the vorticity-vector potential formulation is adopted in order to satisfy the equation of continuity automatically. The Poisson equations for the vector potentials are discretized also with eighth-order accurate method and the higher-order multi-grid method is employed. The accuracy and efficiency of the present Poisson solver are inspected in detail. The present method is, at the outset, applied to computations of cubic cavity flow and the result shows a striking agreement with that using the pseudo-spectral method. After having shown that the present method predicts accurately the three-dimensional instability of plane Poiseuille flow, the numerical simulation of the transient turbulent flow in a plane channel is dealt with in the 653 grid. The result shows an excellent agreement with that using the pseudo-spectral method; so the present computational method is suitable for the numerical simulation of shear flow turbulences.
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