Runge--Kutta

The capabilities of summation-by-parts and structure-preserving operators for compressible computational fluid dynamics and reaction-diffusion models

With the algorithm’s suitability for exploiting current petascale and next-generation exascale supercomputers, stable and structure-preserving properties are necessary to develop predictive computational tools. In this dissertation, …

Relaxation Runge--Kutta Methods: Fully Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier--Stokes Equations

This paper has gained a large traction in the field because it extends the entropy-stability features previously only available at the semi-discrete level to a fully-discrete scheme.