Dimension Splitting Method for 3D Rotating Compressible Navier-Stokes Equations in the Turbomachinery

Abstract

In this paper, we propose a dimension splitting method for Navier-Stokes equations (NSEs). The main idea is as follows. The domain of flow in 3D is decomposed into several thin layers. In each layer, The 3D NSEs can be represented as the sum of a membrane operator and a normal (bending) operator on the boundary of layer. And The Euler central difference is used to approximate the bending operator. When restricting the 3D NSEs on the boundary in each layer, we obtain a series of two dimensional-three components NSEs (called as 2D-3C NSEs). Then we construct an approximate solution of 3D NSES by solutions of those 2D-3C NSEs.