非圧縮性流体解析における差分スキームの保存特性 : 第1報, 解析的要求事項, 離散オペレータの定義, レギュラ格子系の差分スキーム

抄録

The purpose of this research is to construct accurate finite difference schemes for incompressible unsteady flow simulations such as large eddy simulation (LES) or direct numerical simulation (DNS). In the first report, conservative properties of the continuity, momentum and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discretized equations. Convective schemes in a proper set are commutable if the corresponding discretized continuity is satisfied. The proper combination of discretized continuity and pressure terms is required for kinetic energy conservation. The skew-symmetric form is the only proper second-order accurate convective scheme in intuitive convective schemes in a regular grid system. Proper second-order accurate divergence and advective forms are indicated. We need not consider proper rotational form if proper advective form is indicated, since the requirement for the rotational form is that it equals the advective form. Proper fourth-order accurate convective schemes in a regular grid system are obtained from a relatively simple extension of the proper second-order schemes.