Navier-Stokes方程式からの渦法の導出 : 三次元流れ

抄録

A vortex method is used to simulate several flow fields, such as high Reynolds number flows around bluff bodies, jet flows, and the backward-facing step flows. This method has some advantages : it does not require construction of a complex mesh, the algorithm is simple, numerical viscosity is not inherently included, and numerical results agree well with experimental and other numerical results. However, a few models, which do not satisfy the solenoidal condition, have been used in three-dimensional flow problems. The aims of the present paper are to derive a basic equation concerning the vortex method from the three-dimensional Navier-Stokes equations and to determine the relationship between the vortex method and the Navier-Stokes equations. The basic equation is derived as a simple integral form of the vorticity ; the present equation shown that the evolution of vorticity field is obtained by taking the sum of the two effects : stretching of vorticity and viscosity, which are obtained individually. The solenoidal condition is also discussed in detail the initial approximate vorticity field must be solenoidal.