Reduced order model of a convection-diffusion equation using Proper Orthogonal Decomposition

TL;DR

This paper introduces a reduced order modeling approach using Proper Orthogonal Decomposition for simulating 1D Burgers' equation, aiming to simplify complex CFD problems while maintaining accuracy.

Contribution

It provides an accessible implementation of POD for 1D Burgers' equation, discusses its physical interpretation, and explores potential extensions to higher dimensions and other nonlinear PDEs.

Findings

POD effectively reduces model complexity.

The method captures key dynamics of Burgers' equation.

Potential for extension to multi-dimensional systems.

Abstract

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.