高次精度数値計算法による二次元一様等方性乱流の大規模数値シミュレーション

概要

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A new higher order method is devised for the numerical simulation of two-dimensional homogeneous isotropic turbulence. The spatial derivatives of the Navier-Stokes equations are discretized by means of the modified differential quadrature (MDQ) method. The resulting system of ordinary differential equations in time is integrated by the fourth-order Runge-Kutta-Gill (RKG) schemes. The elliptic (Poisson) equation in solved by a new variable-order multigrid method. The direct simulations are presented at resolutions up to 1024×1024. The results suggest that the present higher order method is more efficient, and that the history of the vorticity field consists of three stages, i. e., development, peak, and decay. The corresponding power laws of inertial energy spectrum are k^<-4>, k^<-3>, and k^<-4>, respectively.
1990-08-25