Kyle A. Schau 
(Advisor: Prof. Oefelein] 

will propose a doctoral thesis entitled, 

Development of Kinetic Energy and Entropy Preserving Schemes for Multicomponent Flows with Shocks and Detonations  

On 

Tuesday, June 21 at 4 p.m.  
Montgomery Knight Building 317 
 

Abstract 

The governing equations of inviscid fluid flow are often described by the Euler equations of gas dynamics and involve the evolution of mass, momentum, total energy, and in the case of multicomponent flows, chemical species mass fractions. Beyond the governing equations, analytical and physical relations suggest implied conservation equations not explicitly solved numerically. The numerical treatment of the governing equations can indirectly solve these implied equations in a consistent, or inconsistent, manner. Consistent treatment of these relationships is important to ensure accurate and stable numerical simulations. Examples of implied conservation equations include kinetic energy, internal energy, and entropy. A recent numerical scheme has been proposed to accurately preserve kinetic energy and entropy in smooth, single component, compressible flows. To date, no kinetic energy and entropy preserving scheme can incorporate the presence of multiple chemicals species and discontinuities such as shocks or detonations. This presentation proposes the development of a kinetic energy and entropy preserving scheme to treat multicomponent Euler flow with discontinuities. The work is motivated by the numerical simulation of a Rotating Detonation Rocket Engine, which showed deficiencies in several state-of-the-art solvers’ ability to capture key aspects of the engine performance compared to experimental data, such as primary detonation wave speed. 

Committee 

• 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