Seminar "From Nonlinear (Entropy) Stability Proofs to Production Simulations: Compressible Flow Solvers (with a Brief Detour)"

Title of the seminar: 

From Nonlinear (Entropy) Stability Proofs to Production Simulations: Compressible Flow Solvers (with a Brief Detour)

Abstract:

Robust and hopefully soon predictive simulation of compressible flows, from subsonic to hypersonic, multi-temperature regimes, demands algorithms that are not just accurate and efficient but obey the physics they approximate. This presentation outlines a path "from proofs to FLOP/s": how high-order (variable-order) discretizations, endowed with nonlinear (entropy) stability, become robust, performance-portable solvers on modern computing architectures. We will briefly revisit the history of entropy analysis to motivate why discrete entropy inequalities matter in practice, then show how naïve boundary closures can destroy stability and how entropy-stable boundary conditions restore a global balance. Results will be presented for wall boundary conditions in the compressible Navier–Stokes equations and in resistive magnetohydrodynamics (MHD). A brief detour will discuss structure-preserving schemes for reaction–diffusion and advection–reaction–diffusion systems, highlighting common analytical patterns that carry over across models. Finally, Prof. Parsani will outline extensions to hypersonic flow and share evidence from canonical and engineering test cases that illustrate accuracy, robustness under severe gradients, and efficient, production-grade execution. The overarching message is that respecting the mathematical and thermodynamic structure of the PDEs is not a luxury: it is the near-future sustainable route to solvers that are trustworthy and fast for production use.