本文之研究目的是發展一個數值方法來計算全速域流場。此數值方法使用的統御方程式為非守恆型態的尤拉方程式或可壓縮那維爾-史托克斯方程式。在計算過程中加入二階基本前處理法(Second order primitive preconditioner)修正壓力項，其步驟為先計算顯性解，再以隱性修正法對顯性解作修正。並且配合沉浸邊界法(Immersed boundary method)來計算流場中之固定物體受到流體所施加的力，以及求解整個流場之各種物理量。
在物理問題方面，本文選取了幾個不可壓縮流與可壓縮流問題做計算，共計有: 一維震波管、二維斜震波、二維震波-邊界層交互作用、二維空穴流及二維流體流經圓柱等。本文以上述的算則求解這幾種物理問題，再比對解析解或前人的研究結果，以確認本數值方法的準確性，並對本數值方法的優缺點做分析。

A numerical method is developed to compute all speed flows. In this research, the govening equations used in this method are nonconservative
Euler Equations or compressible Navier-Stokes Equations. The second order primitive preconditioner is included correct the pressure field in the calculated process. Its steps are calculating explicit solutions first, and than correcting the explicit solutions by an implicit correction method. The immersed boundary method is also used to simulate the fluid-particles interaction problems.
On the physics problems, some incompressible and compressible problems are chosen to validate the proposed method . There are one dimensional shock tube, two dimensional oblique shock wave, two dimensional shock-boundary-layer interaction, two dimensional cavity flow, and two dimensional flow over cylinder. In order to track the accuracy of the scheme, we solve those problems by the scheme and compare the results with exact solutions or others’ results. We also analyze the advantages and the faults about the scheme.

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