Model Order Reduction using POD

1. Model Order Reduction using POD Student Researcher: Tony Lau Advisor: Karen Willcox • Motivation • It is difficult to resolve the mean flow characteristics and capture the inherent unsteadiness of an aerodynamic flow. • Project Goals • Through the use of model order reduction, lower order models can be generated that require less computational power yet retain the high level of fidelity of a full order solver. • Proper Orthogonal Decomposition (POD) is the technique used to create the reduced order models.

2. Model Order Reduction using POD • Solutions generated from flow simulations may contain an extensive number of states. • Flow simulations are performed using NASA’s FUN2D, a fully unstructured Navier-Stokes solver • Solution states ( ) may number on the order of 106 for a solution as shown here. • Large and complex simulationsare very computationally costly • Analyzing variations in the flow, such as changing initial conditions, each require a completely new simulation

3. Model Order Reduction using POD • Application of Model Order Reduction • “Snapshots” of the flow are taken from the full order solver. • These snapshots are solutions of the computational model at different instances in time. • Proper Orthogonal Decomposition • The proper orthogonal decomposition determines an optimal set of basis vectors that minimize the error between the exact and projected data. • Reduction achieved may be ofseveral orders of magnitude • This reduced model may be used for further studies, but at a lower computational cost.