Strictly Convex Entropy and Entropy Stable Schemes for the Reactive Euler Equations

Explore advanced mathematical approaches to solving reactive Euler equations in this 39-minute conference talk that addresses fundamental challenges in modeling inviscid compressible flow with chemical reactions. Discover why the classical entropy function associated with thermodynamic entropy loses strict convexity under ideal gas equations of state for hyperbolic systems, and examine two innovative strategies to overcome this limitation. Learn about the first approach involving entropy function correction through the addition of extra terms to create strictly convex entropy functions capable of symmetrizing both reactive Euler and reactive Navier-Stokes equations. Investigate the second strategy of modifying the equation of state itself, revealing a family of non-ideal gas equations that maintain strict convexity of the classical entropy function. Understand how these modified equations satisfy Conservation-Dissipation Conditions for general hyperbolic relaxation systems, ensuring the existence of zero relaxation limits, and examine the elegant eigen-system derivation for the Jacobian matrix under the proposed equations of state. Review numerical experiments demonstrating the capability of the proposed equations to generate ZND detonations, and explore the design of entropy stable discontinuous Galerkin schemes based on the strictly convex entropy function, validated through comprehensive numerical examples.