In this work, a numerical simulation of 1D Burgers' equation is developed using finite difference method and a reduced order model (ROM) of the simulation is developed using proper orthogonal decomposition (POD). The objective of this work is to provide an introduction of the POD method to researchers interested in computational fluid dynamics (CFD). This work discusses a physical interpretation of the POD method, its strengths and shortcomings and an implementation of the algorithm that may be extended to 2D, 3D Burgers' equation and other non-linear partial differential equations (PDE) of this class, to develop models for more complex systems.

翻译：本文采用有限差分法对一维Burgers方程进行数值模拟，并利用本征正交分解（POD）方法构建该模拟的降阶模型（ROM）。本文旨在为计算流体力学（CFD）领域的研究者提供POD方法的基础介绍。文中讨论了POD方法的物理意义、其优势与局限性，并提供了可扩展至二维、三维Burgers方程及此类其他非线性偏微分方程（PDE）的算法实现方法，从而为更复杂系统开发相应模型。