等位函數法是用來處理不可壓縮二相流界面問題的數值方法，而等位函數法把這個界面定義為一個平滑函數的零等位面。 由於等位函數為一平滑函數，為了維持等位函數的特性，將兩流體交界面維持在一微小寬度，密度與黏滯係數也會隨著等位函數而改變。 本篇論文主要以等位函數來處理不可壓縮二相流的界面變化，在求解三維Navier-Stokes方程式的部分，以有限差分法來處理。 由於為二相流，則必須考慮到密度、黏滯係數及雷諾數的的給定方式。數值實驗包括三維水波盪漾問題、液滴落地及落水等問題。 A numerical method using the level set method for solving incompressible two-phase flow with moving interface is discussed in this thesis. The interface is identified as the zero level set of a smooth function. We maintain the level set function as a smooth distance function allowing us to give the interface a thickness fixed in time. Density and viscosity both depend on the level set function being a distance function. In this thesis, we compute incompressible air-water flows using the level set method and solve the three-dimensional incompressible Navier-Stokes equations by the finite difference method. In addition, we consider the density and viscosity. We used a long rectangular lake and a water drop to fall into the ground or fall to the water on three-dimensional as model to observe a change in the interface.
