In this paper, a new algorithm based on differential geometry viewpoint to solve the 3D rotating Navier-Stokes equations with complex Boundary is proposed, which is called Bi-parallel algorithm. For xample, it can be applied to passage flow between two blades in impeller and circulation flow through aircrafts with complex geometric shape of boundary. Assume that a domain in $R^3$ can be decomposed into a series sub-domain, which is called "flow layer", by a series smooth surface $\Im_k, k=1,...,M$. Applying differential geometry method, the 3D Navier-Stokes operator can be split into two kind of operator: the "Membrane Operator" on the tangent space at the surface $\Im_k$ and the "Bending Operator" along the transverse direction. The Bending Operators are approximated by the finite different quotients and restricted the 3D Naver-Stokes equations on the interface surface $\Im_k$, a Bi-Parallel algorithm can be constructed along two directors: "Bending" direction and "Membrane" directors. The advantages of the method are that: (1) it can improve the accuracy of approximate solution caused of irregular mesh nearly the complex boundary; (2) it can overcome the numerically effects of boundary layer, whic is a good boundary layer numerical method; (3) it is sufficiency to solve a two dimensional sub-problem without solving 3D sub-problem.
Navier-Stokes equations and Banach spaces of local measures
这篇论文被arXiv管理员删除，因为它剽窃了“Kozono，Hideo; Shimada，Yukihiro Bilinear estimates in homogeneous Triebel-Lizorkin spaces and the Navier-斯托克斯方程”。数学纳赫276（2004），63- 74. "
