本篇論文目中，我們使用全勢流的方程式，來描述一個跨音速流體，在離散的方法中我們使用了有限差分法和上風密度法，來推導出大型稀疏的非線性方程組。接著詳細說明平行化非線性消去預調節法對牛頓演算法的優勢。最後我們模擬了兩個不同情況的幾何圖形，為NACA0012 的機翼模型和內部通道流的模型，也給出了數值結果，其中包括演算法和總結本文的主要貢獻，並指出此演算法有哪一些潛在的應用。

We describe the model equation for modeling transonic flows based on full potential equation and the derivation of a large sparse nonlinear system of equations using the finite differences with the density upwind technique. And then give a detailed description of the proposed algorithm, a parallel adaptive nonlinear elimination preconditioned inexact Newton algorithm. Last, presents the numerical results, including parallel performance for the algorithm and the paper summarize the main contribution of this paper and point out some potential applications of the algorithm.

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