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

@article{Ranocha2021OptimizedRM,
  title={Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics},
  author={Hendrik Ranocha and Lisandro Dalcin and Matteo Parsani and David I. Ketcheson},
  journal={ArXiv},
  year={2021},
  volume={abs/2104.06836}
}
We develop error-control based time integration algorithms for compressible fluid dynamics (CFD) applications and show that they are efficient and robust in both the accuracy-limited and stability-limited regime. Focusing on discontinuous spectral element semidiscretizations, we design new controllers for existing methods and for some new embedded Runge-Kutta pairs. We demonstrate the importance of choosing adequate controller parameters and provide a means to obtain these in practice. We… 
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