This thesis presents the developments of three-dimensional numerical simulations using different algorithms and finite element types for injection molding filling. For purpose of verification and comparison, two numerical models, the mixed model and the equal-order model, were used to solve the Stokes equations with three different tetrahedral elements (Taylor-Hood, MINI, and equal-order). The results of the Taylor-Hood element were the most accurate although computational times were the largest. The equal-order formulation was more efficient than the mixed formulation with the MINI element in solving the Stokes equations because of the separate approach in solving the velocity and pressure equations.; The control volume scheme with tetrahedral finite element mesh was used for tracking advancing melt fronts and the Operator Splitting method was selected to solve the energy equation. A new, simple memory management procedure was introduced to deal with the large sparse matrix system without using a huge amount of storage space. The numerical simulation was validated for mold filling of a precision lens. The numerical test for the lens part gave reasonable results for fill patterns, velocity, pressure, and temperature fields. The predicted melt front advancement had good agreement with the experimental results. The presence of weld lines before the end of filling was also predicted well in the numerical simulations.; As a new application area, a two-step macro-micro filling approach was adopted for the filling analysis of a part with a micro-surface feature to handle both macro and micro dimensions while avoiding an excessive number of elements. The evaluated filled heights in the micro feature had a good agreement with the experimental data. The filled heights were larger when the flow velocity was higher and the heat transfer coefficient was lower. For more accurate predictions in the micro filling, a variable local heat transfer coefficient is recommended and the analysis should include the effects such as surface tension, wall slip, etc.
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