
Mathematics 2011
Geometry Method for the Rotating NavierStokes Equations With Complex Boundary and the BiParallel AlgorithmAbstract: In this paper, a new algorithm based on differential geometry viewpoint to solve the 3D rotating NavierStokes equations with complex Boundary is proposed, which is called Biparallel 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 subdomain, which is called "flow layer", by a series smooth surface $\Im_k, k=1,...,M$. Applying differential geometry method, the 3D NavierStokes 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 NaverStokes equations on the interface surface $\Im_k$, a BiParallel 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 subproblem without solving 3D subproblem.
