A Geometric Method and Dimension Split Algorithm for The 3-D Compressible Navier-Stokes Equations in Turbomachine
Abstract
In this paper,using classical tensor calculus, we derive the compressible Navier-Stokes Equation on a two dimensional manifold as a stream surface , define stream fuction and derive the equation satisfied by stream function. Based on this a new algorithm is proposaled which is called dimension splite algorithm. This new method is difference from domain decomposition method. In domain decomposition method we have to solve 3-D problem in each subdomain but we solve two dimensional problem in each subdomain only in our new method.A numerical experiment for turbomachinery is devoted.