凝固過程是一個很複雜的問題，其過程參數控制不易，易產生缺陷，影響材料品質。而凝固微結構之數值模擬將有助於了解凝固過程中流場、溫度場與濃度場變化對微結構之影響，提高材料品質。
本文之研究對象為簡單剪力流對成長之網狀晶的影響，利用已建立之自我滿足的網狀晶形狀，建立三維的模型。本文數值方法採用有限元素法，並使用天空線存取模式，以直接的LU分解法來求解溫度場、濃度場與流場聯立方程組。在求解過程中，使用高斯積分法計算聯立方程組中的積分式。另外，流場應用處罰函數法將動量方程式中之壓力以速度取代，減少計算時之複雜程度。

　　計算結果方面，在二、三維問題的測試中，可以證明本數值方法求解流場、溫度場及濃度場之可行性。在三維的網狀晶模擬分析上，於網狀晶頂部之下之流場，由於流場受阻於網狀晶的形狀，簡單剪力流對網狀晶的影響侷限於靠近網狀晶頂部的部分，其餘的部分影響不大。因此，網狀晶成長之溫度與濃度變化主要是沿著成長方向進行，靠近網狀晶液固界面處因潛熱釋放具較高的溫度；而凝固時液固界面會有多餘的溶質釋放，造成液固界面的濃度較高。並且流體的流動會將網狀晶頂部附近上游的溶質帶到下游，使在網狀晶下游的濃度較高；然對溫度場而言，網狀晶頂部附近之流場對其的影響較小。

　　A solidification process is a complicated problem and its control parameters are not easy to handle. Therefore, the defects in the materials during solidification are easily brought out and influence the quality of materials. However, the computer simulation of the solidification microstructures could help analyze their influences in velocity, temperature and concentration fields to enhance the material quality. A three-dimensional model of a cellular growth was built in our work by using the self-consistent cellular shape. The numerical method was the finite element method, in which the skyline storage mode and the LU decomposition method were used to solve the matrix equations. Gauss quadrature integration was adopted to compute the integration formulations and the penalty formulation method, which substituted for the pressure term in the momentum equations, was applied to fluid field to reduce the computational difficulty. From the simulated results, the feasibilities of these methods in velocity, temperature and concentration fields were proved by some tests of specific 2-D and 3-D models. For the 3-D simulation of the cellular growth, the effect of simple shear flow only imposed on the vicinity of the cell tip due to the block of the cell and therefore no obvious influence elsewhere below the vicinity of the tip was observed. For this reason, the temperature and concentration distributions mainly followed the growth direction of the cell. The latent heat release and solute diffusion increased the temperature and concentration respectively at the solidification interface. The fluid flow could bring the solute near the cell tip from the upstream to the downstream to make the latter one have the higher concentration. Contrarily, the fluid flow effect on the temperature field near the cell tip was not obvious.

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