非圧縮性乱流数値解析に適した一般座標系差分スキーム : (第1報, 座標変換後の基礎方程式の解析的保存特性と適切な差分スキームの一般座標系への拡張)

概要

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In order to conduct direct numerical simulation (DNS) or large eddy simulation (LES) of turbulent flows in complicated flow geometry, accurate finite difference methods are needed in generalized curvilinear coordinate system. Recently, it was shown that the analytical conservation properties of the set of basic equations are needed to be satisfied properly even in discretized basic equations in order to obtain accurate and stable solutions in simulations of incompressible turbulent flow using finite difference method. The basic equations treated here are the continuity equation, the Navier-Stokes equation and the transport equations of the square values of velocity components and the kinetic energy. In this paper, finite difference schemes in generalized curvilinear coordinate system that are suitable for simulations of incompressible turbulent flow are constructed from relatively simple extension of the proper finite difference schemes derived in equidistant Cartesian coordinate system. The extension of finite difference scheme into generalized curvilinear coordinate system is based on the fact that the analytical conservation properties of the coordinate transformed basic equations for incompressible viscous flows are identical with that in Cartesian coordinates.
一般社団法人日本機械学会の論文
1999-05-25