Low-dissipation and low-dispersion Runge-Kutta schemes for computational acoustics
Journal of Computational Physics
2N-storage low dissipation and dispersion Runge-Kutta schemes for computational acoustics
Journal of Computational Physics
Optimal Runge-Kutta methods for first order pseudospectral operators
Journal of Computational Physics
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Short note: a new minimum storage Runge-Kutta scheme for computational acoustics
Journal of Computational Physics
Journal of Computational Physics
Time step restrictions for Runge-Kutta discontinuous Galerkin methods on triangular grids
Journal of Computational Physics
High-accuracy large-step explicit Runge-Kutta (HALE-RK) schemes for computational aeroacoustics
Journal of Computational Physics
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
Journal of Computational Physics
High-Order Local Time Stepping on Moving DG Spectral Element Meshes
Journal of Scientific Computing
Hi-index | 31.45 |
We study time step restrictions due to linear stability constraints of Runge-Kutta Discontinuous Galerkin methods on triangular grids. The scalar advection equation is discretized in space by the Discontinuous Galerkin method with either the Lax-Friedrichs flux or the upwind flux, and integrated in time with various Runge-Kutta schemes designed for linear wave propagation problems or non-linear applications. Von-Neumann-like analyses are performed on structured periodic grids made up of congruent elements, to investigate the influence of element shape on the stability restrictions. We assess CFL conditions based on different element size measures, among which only the radius of the inscribed circle and the shortest height prove appropriate, although they are not totally independent of the triangle shape. We explain their general behaviour with respect to element quality, and report the corresponding Courant numbers with both types of flux and polynomial order p ranging from 1 to 10, for use as guidelines in practical simulations. We also compare the performance of the Lax-Friedrichs flux and the upwind flux, and we draw general conclusions about the relative computational efficiency of RK schemes. The application of CFL conditions to two examples involving respectively an unstructured and a hybrid grid confirms our results, although it shows that local stability criteria tend to yield too restrictive conditions.