Ayoub Gouasmi, PhD Candidate, Aerospace Engineering


Entropy-Stable (ES) schemes have gathered a lot of attention over the last decade, especially in the context of under-resolved simulations of compressible turbulent flows, where high-order accuracy and robustness are difficult to simultaneously achieve. ES schemes can enforce a non-decreasing total entropy, in agreement with the second principle of thermodynamics. However, several challenges remain to their practical use.

The current state-of-the-art of ES schemes solves the Navier-Stokes equations for a single-component perfect gas in chemical and thermal equilibrium. This model is not appropriate in applications such as hypersonics and combustion. As a first step towards enabling such applications, we constructed ES schemes for the multicomponent compressible Euler equations. Along the way, we also extended a theoretical result on the correct local behavior of entropy-stable approximations.

While entropy-stability is valuable, it does not imply a well-behaved solution. To better understand how ES schemes may or may not improve solution quality, we revisited, in terms of entropy, two classical shock-capturing problems where stability is not the core issue. We studied the overheating anomalies typically encountered in shock reflection simulations, and the severe accuracy degradation issues of upwind-type schemes in the low Mach regime.


Dissertation Committee:

Chair: Prof. Karthik Duraisamy
Cognate Member: Prof. Smadar Karni
Members: Prof. Philip L. Roe, Prof. Eitan Tadmor (University of Maryland), Dr. Scott M. Murman (NASA Ames Research Center)