本研究以漸增壓力投影法來建立一不可壓縮之光滑粒子水動力模式，並以Rayleigh-Benard自然對流問題做為本模式之驗證。比較結果顯示本研究所建立之不可壓縮光滑粒子水動力模式可以準確預測此一對流熱傳問題。接著此不可壓縮光滑粒子水動力模式被應用於求解一方形密閉空間一加熱圓柱所引起的自然對流問題，與其他模式對此問題之模擬結果相比，本研究所建立之不可壓縮之光滑粒子水動力模式所得之結果很接近其他的結果。為探求是否旋轉此一圓柱可增進風閉空間內的熱傳，因此本模式並模擬一旋轉加熱圓柱所引起之混合對流，結果顯示在特定條件下，外加之圓柱旋轉動能並沒有增加熱傳效果。由所得數值結果可知，本研究所建立之不可壓縮光滑粒子水動力模式可在不需重新生成網格的情形下模擬具複雜及移動邊界之熱傳問題。

An incompressible smoothed particle hydrodynamics (ISPH) method based on the incremental pressure projection method is developed in this study. The Rayleigh-B\'enard convection in a square enclosure is used as a validation case and the results obtained by the proposed ISPH model are compared to the benchmark solutions. The comparison shows that the estabished ISPH method has a good performance in terms of accuracy. Subsequently, the proposed ISPH method is employed to simulate natural convection from a heated cylinder in a square enclosure. It shows that the predictions obtained by the ISPH method are in good agreements with the results obtained by previous studies using alternative numerical methods. A rotating and heated cylinder is also considered to study the effect of the rotation on the heat transfer process in the enclosure space. The numerical results show that for a square enclosure at Ra/Re_D^2 ≥ 1.0, the addition of kinetic energy in the form of rotation does not enhance the heat transfer process. In terms of results, it turns out that the proposed ISPH model is capable to simulate heat transfer problems with the complex and moving boundaries without adapting a mesh.

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