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:在这项工作中,利用有限差异法开发了1D汉堡方程式的数字模拟,并利用适当的正心分解(POD)开发了模拟的减序模型(ROM),目的是向对计算流体动态感兴趣的研究人员介绍POD方法。这项工作讨论了对POD方法的物理解释、其优点和缺点以及可扩展至该类2D、3D汉堡方程式和其他非线性局部方程式的算法的实施,以便为更复杂的系统开发模型。</s>