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On the Strong Stability Preserving Property of Runge-Kutta Methods for Hyperbolic Problems
Mohammad R. Najafian, Brian C. Vermeire
Strong Stability Preserving (SSP) time integration schemes maintain stability of the forward Euler method for any initial value problem. However, only a small subset of Runge-Kutta…
Quasi-Orthogonal Runge-Kutta Projection Methods
Mohammad R. Najafian, Brian C. Vermeire
A wide range of physical phenomena exhibit auxiliary admissibility criteria, such as conservation of entropy or various energies, which arise implicitly under exact solution of the…
Hybridized Implicit-Explicit Flux Reconstruction Methods
Carlos A. Pereira, Brian C. Vermeire
For turbulent problems of industrial scale, computational cost may become prohibitive due to the stability constraints associated with explicit time discretization of the underlyin…
Energy Conservative Relaxation-Free Runge-Kutta Schemes
Mohammad R. Najafian, Brian C. Vermeire
A wide range of physical phenomena exhibit auxiliary admissibility criteria, such as conservation of entropy or various energies, which arise implicitly under the exact solution of…
Hybridized Formulations of Flux Reconstruction Schemes for Advection-Diffusion Problems
Carlos A. Pereira, Brian C. Vermeire
We present the hybridization of flux reconstruction methods for advection-diffusion problems. Hybridization introduces a new variable into the problem so that it can be reduced via…