非結構性寬頻元素法應用於含曲面的LED之熱傳模擬

Abstract

本文主旨在於擴充應用在非結構性網格之寬頻元素法程式的功能，使之能夠模擬常見的熱傳問題，這些功能包括元素分類、處理熱對流邊界的能力以及讓程式可適應三維的彎曲幾何外型。寬頻元素法是一種高階的數值方法，若不以高階的方法來處理彎曲邊界，則會降低寬頻精確的性質，在本文中，以邊界的展開模式來得到彎曲元素與標準元素的映射方程式，透過許多例子驗證其寬頻精確性，最後以此程式來模擬LED light bar的熱傳問題。

The object of this study is to expand the functions of the code with unstructured hp spectral element method. The developed code can simulate common heat transfer problems. Theses functions are element classification, the ability to deal with heat convectional boundary conditions, and making the code accommodate three dimensional curved geometry. Spectral element method is a high-order numerical method. If curved geometry is not interpolated with high-order method, it cannot reduce spectral accuracy. In this thesis, we get the mapping function of the curved element with boundary modes. And the code was validated by several examples. Finally, we take this code to simulate the heat transfer problem of a LED light bar.