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

@article{Ranocha2020RelaxationRM,
  title={Relaxation Runge-Kutta Methods: Fully Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier-Stokes Equations},
  author={Hendrik Ranocha and Mohammed Sayyari and L. Dalc{\'i}n and M. Parsani and D. Ketcheson},
  journal={SIAM J. Sci. Comput.},
  year={2020},
  volume={42},
  pages={A612-A638}
}
  • Hendrik Ranocha, Mohammed Sayyari, +2 authors D. Ketcheson
  • Published 2020
  • Mathematics, Computer Science
  • SIAM J. Sci. Comput.
  • The framework of inner product norm preserving relaxation Runge-Kutta methods (David I. Ketcheson, \emph{Relaxation Runge-Kutta Methods: Conservation and Stability for Inner-Product Norms}, SIAM Journal on Numerical Analysis, 2019) is extended to general convex quantities. Conservation, dissipation, or other solution properties with respect to any convex functional are enforced by the addition of a {\em relaxation parameter} that multiplies the Runge-Kutta update at each step. Moreover, other… CONTINUE READING
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