Bounding Methods in Computational Fluid Dynamics for use in a Sequential Decision Process

Open Access
Valenti, Justin D
Graduate Program:
Aerospace Engineering
Master of Science
Document Type:
Master Thesis
Date of Defense:
July 31, 2017
Committee Members:
  • Michael P Kinzel, Thesis Advisor
  • Simon Walter Miller, Committee Member
  • Mark David Maughmer, Committee Member
  • Philip John Morris, Committee Member
  • Computational Fluid Dynamics
  • Sequential Design Process
  • Trade Space Exploration
  • Design
  • Sequential Design
  • Bounding
  • Numerical Uncertainty
  • Discretization Uncertainty
This thesis aims to couple Computational Fluid Dynamics (CFD) with the Sequential Decision Process (SDP) to perform trade space exploration. To do so, methods are developed to "bound" CFD calculations. Two approaches are taken to bound these calculations: (1) a physics based method and (2) a numerical uncertainty based method. The physics based method uses the specific governing physics of the simulation to ensure that the calculations are bounding of the "true" result from above or below. The numerical uncertainty based approach uses standard methods to quantify uncertainty due to discretization. This uncertainty is, then, used to provide bounding results of "true" value for the SDP. These methods are applied to the aerodynamic shape design of a low Reynolds Number fuselage pod. The first preliminary attempt at an SDP uses the physics based approach. A 3-parameter 2-model fidelity level design process is used, demonstrating the SDP discriminatory ability using physics based bounding. A more formal SDP is done using the uncertainty based approach. In this second attempt, 7 mesh densities defined 7 levels of model fidelities. A 2-parameter design study was performed over the 7-model fidelities and an optimal policy was both predicted prior to the design study and found in post processing. This work is a first attempt to use CFD as the analysis tool in an SDP and is expected to provide insights that generalize to other numerical methods for use with the SDP.