Model Reduction for a Pulsed Detonation Combuster via Shifted Proper Orthogonal Decomposition
This work addresses the need for efficient model reduction in transport-dominated fluid dynamics, offering a significant improvement over classical POD for such systems.
The authors propose a new algorithm for shifted proper orthogonal decomposition (sPOD) to handle transport-dominated systems, demonstrating on a pulsed detonation combuster that sPOD requires ten times fewer modes than POD for the same accuracy and better captures moving front profiles.
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.