Lie微分による流れ場の支配方程式 : 数値計算のための自然標構表現(微分幾何学)

概要

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I reconstructed the equations governing the motion of a fluid with the Lie derivative in the flat manifold. The equations resulting from this theory of the differential geometry are of exactly the same shape as the Navier-Stokes equation, it follows from this that the NS includes a condition applying in the laminar flow fields, it is questionable whether this equation applies in the turbulent flow fields. I think that another mechanism lurks within the turbulent flow, such as new viscous hypotheses instead of the Navier-Poisson's law or the Stokes's relation, and that the flat manifold is distorted by these metric tensors. but there is not sufficient evidence, it is neccessary to investigat on this point. And moreover, I think that a coordinate suitable for the streamline which is obtained as a unigue solution satisfying the governing equations in the laminar flow field is one along the streamline, from this idea, I represented those governing equations obtained by the Lie derivative with the natural frame.
広島文化学園大学の論文
1998-11-01