PhD Defense by Kyle A. Schau

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Kyle A. Schau
Advisor: Prof. Joseph Oefelein

will defend a doctoral thesis entitled,

A Kinetic Energy Preserving and Entropy Conserving Schemes for Stable Simulation of Fluid Flow


Friday, October 6 at 12 p.m.
Montgomery Knight Building 317



The evolution of physical systems is often described by basic conservation principles. For example, the Euler and Navier-Stokes Equations approximate the spatial-temporal evolution of inviscid and viscous fluid flow, respectively. These equations derive from the simple principles of conservation of mass, momentum, and energy (and chemical species for multicomponent flows.). The discrete, numerical approximations of these conservation equations can take many, well studied forms. While conservation is an important physical concept to replicate numerically, it does not guarantee accuracy, or stability. In fact, a scheme developed with only conservation in mind will almost certainly suffer from numerical errors and instability, even for trivial simulations. Accuracy and stability improvements have therefore been at the forefront of improving numerical methods for decades. One such method to improve accuracy and stability is the adherence of numerical methods to implied governing equations. As in, behavior derived from the analytical conservation equations, but not explicitly solved for in a simulation. Two such examples are the evolution of kinetic energy and entropy. Both of these physical quantities have defined behavior from the analytical equations. Ensuring a numerical system of equations also adheres to this behavior can result in improved stability and accuracy.  This work develops a fully discrete numerical method for solving the Euler equations which preserves the accurate evolution of kinetic energy, and is formally entropy conservative, termed KEPEC. The presented scheme improves upon the stability and accuracy of existing methods. The scheme is then extended to multicomponent flow however, the analytical behavior of entropy conservation is not straightforward in fully conservative, multicomponent flows. Finally, a shock capturing extension of the presented scheme is designed from kinetic energy preserving and entropy stability principles. The scheme demonstrates the ability to resolve shocks, and provides a novel method for prescribing entropy evolution behavior.



  • Prof. Joseph Oefelein– School of Aerospace Engineering (advisor)
  • Prof. Timothy Lieuwen– School of Aerospace Engineering
  • Prof. Vigor Yang – School of Aerospace Engineering
  • Prof. Jerry Seitzman– School of Aerospace Engineering
  • Prof. Yingjie Liu– School of Mathematics
  • Prof. Ellen Mazumdar – School of Mechanical Engineering


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    Tatianna Richardson
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    Tatianna Richardson
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