外部绕流的Navier-Stokes方程的边界层方程和维数分裂法

Boundary layer equations and a dimensional split method for Navier-Stokes equations in exterior flow around an obstacle

采用基于物体表面二维曲面的半测地坐标系(S-coordinate)建立了一个新的外部绕流边界层方程(boundary layer equations,BLE).BLE是一个关于物体的未知法向粘性应力张量和压力的非线性偏微分方程,其解的存在性得到了证明.此外,通过在二维流形上应用若干个2D-3C偏微分方程组来近似Navier-Stokes方程,获得了三维Navier-Stokes方程的维数分裂法.最后,对球和椭球的外部绕流问题给出了算例.

New boundary layer equations （BLEs） for exterior flow around a body, are established using a semi-geodesic coordinate system （S-coordinate） based on the curved two dimensional surface of the body. BLEs are nonlinear partial differential equations on unknown normal viscous stress tensor and pressure on the surface. In addition, a dimensional split method for three dimensional Navier- Stokes equations in exterial domain around an obstacle is developed by applying several 2D-3C partial differential equations on two dimensional manifolds to approximate 3D Navier-Stokes equations. Numerical examples for the exterior flow around a spheroid and ellipsoid are presented here.