Graphic Presentation of Chaos Generated in Computational Fluid Dynamics

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概要

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• A method is proposed to graphically display the instability in the numerical solution of fluid dynamic equation. The Navier-Stokes equations are modified, based on the assumption that the pressure gradient is proportional to the gradient of kinetic energy. Modified partial differential equations are expressed only in terms of velocity components. The resulting differential equations are approximated by the finite differences with respect to space variables, where asymmetrical finite difference has been applied to some terms. A set of ordinary differential equations with time are obtained. This set of equations is numerically solved by the Eulerian scheme with a finite time step. The magnitudes of the kinetic energy at every mesh point are displayed on a graphics screen. The numerical method is applied to a problem corresponding to a two-dimensional unsteady state fluid flow around an obstacle, suddenly put into a uniform fluid flow stream. The number of 2(X) by 400 mesh points in the discretization are large enough to simulate the vortex shedding behind the obstacle. Chaos can be observed in the wake, owing to the propagation of numerical integration errors, at large time step. The lower limit of the time step for the generation of chaos is determined by numerical experiments.

• 一般社団法人情報処理学会の論文
• 1992-03-31

著者

• Aratani Toshiro

  Department Of Management And Information Sciences Hiroshima Prefectural University

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