Navier-Stokesの方程式の一般曲線座標系表示

概要

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Recently, by using the numerical calculation methods such as the finite difference method, it is in the way of steady progress to evaluate quantitatively the flow fields around a body, which can not be elucidated clearly by the analytical procedure. Then, in order to improve the accuracy, the fundamental equations of hydrodynamics in this case are represented by applying the general curvilinear coordinate system fitted to the body surface. In this paper, at first, these equations are expressed in the perfect tensor form based on the differencial geometry, and are proved to agree analytically with those adopted in the practical numerical calculation methods recently. Next, concerning water with the free surface, the fundamental equations, the equations of the initial and boundary conditions and the expressions of the forces acting on the body are presented in the tensor form under the general curvilinear coordinate system, and then the relation between the eddy viscosity and the Smagorinsky turbulent model is explained briefly. At last, the fundamental equations are expressed for the moving axes and the k-ε turbulent model.
社団法人日本船舶海洋工学会の論文
1988-03-22