SUMMARYIn this paper, by using classical tensor calculus, we derive the compressible Navier-Stokes equation on a so-called stream surface which is a two-dimensional (2-D) manifold that gives a deÿnition of a stream function with the equation satisÿed by it. Based on this, a new algorithm is proposed which is called dimension split algorithm. This new method is di erent from the domain decomposition method. In the domain decomposition method, we have to solve a three-dimensional problem in each subdomain but we solve a 2-D problem in each subdomain. A numerical experiment for the turbomachine is provided.
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