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

The framework of inner product norm preserving relaxation Runge--Kutta methods [D. I. Ketcheson, SIAM J. Numer. Anal., 57 (2019), pp. 2850--2870] is extended to general convex quantities. Conservation, dissipation, or other solution properties with …