My name is Mohammed Sayyari; I work on entropy-stable high-order discretizations using the summation-by-parts (SBP) and simultaneous-approximation-terms (SAT) framework. My main model of interest is the compressible Navier–Stokes equations. Currently, I am focusing on a regularization approach for the Navier–Stokes equations for high-speed flows. This lead to the development of novel enropy-stable high-order isothermal wall boundary conditions necessary to verify the new regularization approach. Recently, I worked on extending the positivity-preserving framework for this model to implicit dual time-stepping schemes overcoming some of the stiffness issues (Sayyari and Yamaleev 2026).

The goals of my scientific endeavor is to apply my math and methods towards sustainabilty effors. This focus is mainly of developing efficient and robust schemes for relevant models via the SBP-SAT approach. To realize this aim, I plan to develop schemes for relevant applications to understanding new weather patterns in the context of climate change and extreme weather events. Two cases come to mind, the first is hurricane simulation, and the second is wild fires. The current High-Performance Computing (HPC) capabilities will be essential, and, thus, are at the center of current research efforts.

I love teaching, and I am passionate about pedagogical innovations that engage my students and drive them to think critically. My teaching experience spans undergraduate general education courses to graduate courses in Computational Fluid Dynamics (CFD) and numerical methods. In Numerical Methods for Internal Aerodynamics (link), I had the pleasure to develop a course from the bottom up, deciding a curriculum, writing slides, python homework assignments, and an oral exam typical of a graduate course in Ruhr-Universität Bochum. Currently, I am enjoying teaching PreCalcI for the second semester at Old Dominion University (link). While the general course is coordinated by the department, I implemented some teaching stratigies that students loved, such as the problem sprints (example 1), and one that only a few brave students attempted, the explain and reflect activity (link). I remain fully prepared to develop courses from my current research, and I can’t wait to take up typical courses such as Calculus, ODEs, and PDEs, or more enjoyably, numerical analysis!