Ph.D. Defense

Scott Theuerkauf

(Advisor: Prof. Oefelein)

"Investigation of Explicit Residual Filtering for LES of the Compressible Navier-Stokes Equations"

Thursday, November 16

12:00 p.m.

Montgomery Knight Building 317

Abstract

Large Eddy Simulation (LES) is a useful tool for modeling turbulent, non-statistically-stationary flow without resolving the entire range of turbulent scales.  While it is frequently calculated using the implicit filter applied by the numerical discretization used to solve the equations of flow, another form of LES uses an explicitly-defined filter to control the range of scales present in the flow.  This method seeks to decouple the LES solution from the grid and numerical method to effectively eliminate competition between the required subfilter-scale (SFS) models and the numerical discretization errors.  Several methods for Explicitly Filtered LES (EFLES) have been attempted in the past with this goal and others in mind.  This work uses a familiar method, grounded in novel derivation from the Navier-Stokes equations governing compressible, reacting flows.  By applying a discrete, sufficiently commuting, low-pass filter that is sufficiently sharp and wide relative to the filtering effects of the underlying numerical scheme to the numerical residual of each equation, the effects of the implicit filter can be minimized, overriding them with those of the explicitly-defined filter.  Additionally, by applying the filter once to each equation, the cost of successive filter operations is minimized, reducing the cost of EFLES.  Finally, the structure of this method allows existing Implicitly Filtered LES (IFLES) numerical methods to be adapted to EFLES in a straightforward and computationally efficient manner.  This work validates this EFLES method on a Taylor-Green Vortex for both incompressible and compressible cases.  A stability analysis examines the requirement to apply a residual filter as part of the EFLES method to each conservation equation and explores the stabilizing effects of residual filtering.  Identifying the computational costs of this approach in context with its advantages provides the advanced knowledge necessary to achieve grid- and scheme-independent results using EFLES for more advanced flows.

Committee

• Prof. Joseph Oefelein – School of Aerospace Engineering (advisor), Georgia Institute of Technology
• Prof. Vigor Yang – School of Aerospace Engineering, Georgia Institute of Technology
• Prof. Pui Kuen Yeung – School of Aerospace Engineering, Georgia Institute of Technology
• Prof. Yingjie Liu – School of Mathematics, Georgia Institute of Technology
• Dr. Ayaboe Edoh – Research Engineer, Jacobs Engineering, Inc.