Model Order Reduction using POD

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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.

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Model Order Reduction using POD

• Solutions generated from flow simulations may
  contain an extensive number of states.
• Flow simulations are performed using NASAs
  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

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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.