h-index: 5 | i10-index: 2 | citations: 206 (upto December 2025)

My name is Mohammed Sayyari; I work on the regularization of the Navier-Stokes and positivity-preserving provably stable high-fidelity numerical schemes for the Navier-Stokes equations as a postdoc in the Department of Mathematics and Statistics at Old Dominion University. With a strong background in computer science, my current project integrates efficient and scalable computation with rigorous mathematical analysis to preserve the stable structure of the underlying model. Through international collaborations, I have contributed to impactful research, such as in the relaxation Runge-Kutta method, where we extended the method to include nonlinear convex functionals such as mathematical entropy. This method provides provable stability for fully-discrete schemes, in contrast to the stability of only the discrete spatial operators, common in this area of research. My long-term research plan is to develop provably stable, robust, and efficient schemes on high-performance computing (HPC) platforms for problems in fire simulation and numerical weather prediction (NWP). These schemes enhance the accuracy and stability of simulations for critical applications like climate modeling and aerospace engineering.

In addition to my research, I have consistently been passionate about teaching. Even when it was not required, I served as a Teaching Assistant during my PhD for a variety of courses spanning computer science and mathematics. For example, I assisted in creating homework and held office hours for courses such as Numerical Analysis of PDEs and Numerical Optimization. Additionally, I inaugurated the course of Numerical Methods for Internal Aerodynamics at Ruhr-Universität Bochum, creating all the course content, from slides and notes to a unique problem set and computer programming examples. I am committed to continuing learning and researching pedagogical methods. For example, I attended a course on the eight practices in teaching mathematics, where I learned key practices such as productive struggle, purposeful questioning, and eliciting evidence of student thinking.