在這篇文章我們考慮尤拉方程式在接近音速流量無變化可壓縮的管，在方程式出現的壓力項和管的位置有關。我們對這柯西問題的方程式，去架構一個區間的逼近解，這個逼近解是由黎曼問題的基本波和線性化方程式的逼近解所組合架構，線性化方程式的逼近解藉由使用”operator splitting”來架構。

In this paper we consider the compressible Euler equations of uniform duct in transonic flow. The pressure term appearing in the equations is also dependent on the location of the duct, which is considered as the product of the density of flow and a function of space. We construct a local approximate solution for the Cauchy problem of equations. This approximate solution is constructed as a combination of homogeneous elementary waves to the Riemann problem and an approximate solution of the linearized equations. The approximate solution of the linearized equations is constructed by the scheme of the
operator splitting.

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