Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics

We develop error-control based time integration algorithms for compressible fluid dynamics (CFD) applications and show that they are efficient robust in both the accuracy-limited stability-limited regime. Focusing on discontinuous spectral element semidiscretizations, we design new controllers existing methods some embedded Runge-Kutta pairs. demonstrate importance of choosing adequate controller parameters provide a means to obtain these practice. compare wide range error-control-based methods, along with common approach which step size control is Courant-Friedrichs-Lewy (CFL) number. The optimized give improved performance naturally adopt close maximum stable CFL number at loose tolerances, while additionally providing temporal error tighter tolerances. numerical examples include challenging industrial CFD applications.