本文之目的在於以數值方法來模擬計算全速域流場現象，並在有黏滯性之不可壓縮流場內，研究並探討流體和粒子之間的交互作用對流場所產生的影響。計算方法以有限體積法來計算可壓縮奈威爾-史托克方程式(Navier-Stokes equations)，並加入二階準確度之基本前處理法，去修正壓力項，使得本數值方法可求解可壓縮和不可壓縮流場之全速域流場。本方法同時使用LLF和AUSM+兩個方法求解介面數值通量。在計算流體與粒子的交互作用，則使用沉浸邊界法來模擬粒子的流場現象。
　　在物理方面，首先選取了幾個簡單的例子：一維震波管流場、無黏滯性可壓縮流的斜震波反射、斜震波與邊界層的交互作用、有黏滯性不可壓縮流的方形空穴流場和流體流過一圓柱，來驗證本文數值方法之正確性，並探討雷諾數和黏滯係數對流場的影響。最後使用沉浸邊界法來模擬和探討粒子墜落運動和兩粒子墜落、碰撞、滾轉運動。

A numerical method is developed to solve all speed flows. The method is applied to simulate the fluid field of the fluid-particle interaction.The numerical method uses a finite volume method to solve the compressible Navier-Stokes equations. Moreover, the second-order primitive preconditioner method is applied to correct the pressure field, which can effectively solve all speed flows including the compressible and incompressible flows.The numerical method also uses the LLF and AUSM+ methods to solve the fluxes at the surface interface. About the fluid-particles interaction, the immersed boundary (IB) method is used to simulate the flow field.

Several problems are chosen: Shock tube problem, oblique shock reflection problem, oblique shock and boundary layer interaction, cavity flow , viscous flow past a circular cylinder, a particle drafting due to gravity force , and two particle flow. First, the numerical method is verified on several problems. Then, the numerical method coupling with the IB method is used to investigate the fluid fields of a particle drafting due to gravity force and two particle flow

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