本研究採用晶格波茲曼法（Lattice Boltzmann Method，LBM），晶格波茲曼法是近年來具前瞻性的數值運算方法，其為介於巨觀與微觀尺度間的介觀尺度模擬方法，適於模擬流場在微小模型中的情形，且其擁有較易模擬兩相流的優點，因此本研究將其應用於微射出成型中的填充過程上。本文主要分為兩個部分，一為引入單相自由表面（Free surface）於晶格波茲曼法中，自由表面可模擬氣相與液相之間的介面現象，因此用此優點模擬出塑料與空氣分離的介面流動現象。二為於熱晶格波茲曼法（Thermal Lattice Boltzmann Method，TLBM）中引入自由表面且模擬溫度場，但由於熱晶格波茲曼法本身的限制，其無法模擬具高普朗特數的流場，因此本文同時分析不同普朗特數下高黏度流體的熱傳問題。

The Lattice Boltzmann Method is a promising numerical method developed in recent years. It is suitable for simulating the flow field in a micro-scale model. Lattice Boltzmann Method has many advantages as it is easy to model the problems of the multi-phase flow, flow with surface tension, flow in porous medias, etc. In this study, we apply it to simulate the behavior of mold filling process in micro injection molding.
This study can be divided into two parts. In the first part, we adopt an algorithm to perform free surface flow simulations with the Lattice Boltzmann Method. The method of Free Surface Method can handle the complex interaction between gas and liquid phases. We use this feature to simulate the interface between polymer and gas. In the second part, we combine free surface method and Thermal Lattice Boltzmann Method to analyze the temperature variation in the filling flow. Due to some restrictions in Thermal Lattice Boltzmann Method model, e.g., high Prandtl number and high viscosity problems, we introduced a new parameter into the Modified Lattice Boltzmann scheme for the simulations.

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