在流體體積法中使用高解析離散法計算兩相流

Abstract

在本研究中將建立ㄧ種直接模擬兩相流的數值方法。在此方法中，藉由求解流體體積分率的傳輸方程式，來抓取兩流體間的介面運動。在本研究中將討論許多數值的離散法，像是高解析離散法和壓縮式離散法。高解析離散法可以維持兩流體間界面的外形，卻沒有辦法減少在介面上的數值擴散。而壓縮式離散法可以達到較少的數值擴散，卻會造成介面形狀的變形。為了處裡上述的問題，大部分混合離散法都是採用一個與介面斜率相關的轉換函數，在高解析離散法和壓縮式離散法之間做切換。本研究主要的目的是在於發展一種在 modified MUSCL 和 modified bounded downwind scheme 之間轉換的混合離散法。此方法在本文中所測試的案例中都有相當高的準確性，而且本方法可以在三角形和四邊形的網格系統中使用。

A numerical method for direct simulations of two-fluid flows is established in this study. The motion of the interface is captured by the solution of a transport equation for the volume fraction. Some numerical schemes, such as high resolution and compressive schemes are discussed in this study. The high resolution schemes preserve the shape of the interface but can not reduce the numerical diffusion. The compressive schemes are able to reach less numerical diffusion but let the interface deformed. Most composite schemes switch the compressive scheme and high resolution scheme with a switching function about the slope of the interface in order to overcome the above problem. The aim of this study is to develop a composite of the modified MUSCL and modified bounded downwind scheme with a switching function. This scheme presents the high accurate results in test cases and can be used on the quadrilateral and triangular mesh.