Model Reduction for a Pulsed Detonation Combuster via Shifted Proper Orthogonal Decomposition

TL;DR

This paper introduces a shifted proper orthogonal decomposition (sPOD) algorithm tailored for transport-dominated systems, demonstrating its efficiency in modeling a pulsed detonation combustor with fewer modes than traditional POD.

Contribution

The paper presents a novel sPOD algorithm that effectively captures transport phenomena by shifting modes, outperforming classical POD in efficiency and accuracy for combustion simulations.

Findings

sPOD requires fewer modes than POD for accurate approximation

sPOD modes better reflect moving front profiles

The algorithm successfully models a pulsed detonation combustor

Abstract

We propose a new algorithm to compute a shifted proper orthogonal decomposition (sPOD) for systems dominated by multiple transport velocities. The sPOD is a recently proposed mode decomposition technique which overcomes the poor performance of classical methods like the proper orthogonal decomposition (POD) for transport-dominated phenomena. This is achieved by identifying the transport directions and velocities and by shifting the modes in space to track the transports. Our new algorithm carries out a residual minimization in which the main computational cost arises from solving a nonlinear optimization problem scaling with the snapshot dimension. We apply the algorithm to snapshot data from the simulation of a pulsed detonation combuster and observe that very few sPOD modes are sufficient to obtain a good approximation. For the same accuracy, the common POD needs ten times as many modes and, in contrast to the sPOD modes, the POD modes do not reflect the moving front profiles properly.