中文摘要：

本文用奇值分解和特征投影分解（proper orthogonal decomposition，简记为POD）研究热传导对流方程，导出其基于POD的一种简化的差分格式，并分析通常的差分格式的解和基于POD的简化的差分格式的解之间的误差估计．最后用方腔流数值例子验证本文的理论的正确性，从而验证了用基于POD的简化的差分格式解热传导对流方程的有效性．

英文摘要：

In this work, the nonstationary conduction-convection equations are studied with singular value decomposition and proper orthogonal decomposition （POD）, A reduced finite difference scheme （FDS） based on POD for the nonstationary conduction-convection equa- tions is presented. And the error estimates between usual finite difference solutions and POD solutions of reduced FDS are analyzed. It is shown by considering the results obtained for numerical simulations of cavity flows that the errors between POD solutions of reduced FDS and usual finite difference solutions are consistent with theoretical results. Moreover, it is also shown that POD method is feasible and efficient in numerical solutions for the nonstationary conduction-convection equations.