Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws
Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
Runge--Kutta Discontinuous Galerkin Method Using WENO Limiters
SIAM Journal on Scientific Computing
Finite-volume WENO schemes for three-dimensional conservation laws
Journal of Computational Physics
SIAM Journal on Scientific Computing
Journal of Scientific Computing
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
Journal of Computational Physics
Journal of Scientific Computing
Development of low dissipative high order filter schemes for multiscale Navier-Stokes/MHD systems
Journal of Computational Physics
Discontinuous Galerkin methods for the chemotaxis and haptotaxis models
Journal of Computational and Applied Mathematics
On the role of Riemann solvers in Discontinuous Galerkin methods for magnetohydrodynamics
Journal of Computational Physics
Nonuniform time-step Runge-Kutta discontinuous Galerkin method for Computational Aeroacoustics
Journal of Computational Physics
A Runge-Kutta discontinuous Galerkin approach to solve reactive flows: The hyperbolic operator
Journal of Computational Physics
A Runge-Kutta discontinuous Galerkin approach to solve reactive flows: The hyperbolic operator
Journal of Computational Physics
Interior penalty DG methods for Maxwell's equations in dispersive media
Journal of Computational Physics
Journal of Computational Physics
Alternating Evolution Schemes for Hyperbolic Conservation Laws
SIAM Journal on Scientific Computing
Journal of Computational Physics
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Runge-Kutta discontinuous Galerkin (RKDG) method is a high order finite element method for solving hyperbolic conservation laws employing useful features from high resolution finite volume schemes, such as the exact or approximate Riemann solvers serving as numerical fluxes, TVD Runge-Kutta time discretizations, and limiters. In most of the RKDG papers in the literature, the Lax-Friedrichs numerical flux is used due to its simplicity, although there are many other numerical fluxes which could also be used. In this paper, we systematically investigate the performance of the RKDG method based on different numerical fluxes, including the first-order monotone fluxes such as the Godunov flux, the Engquist-Osher flux, etc., and second-order TVD fluxes, with the objective of obtaining better performance by choosing suitable numerical fluxes. The detailed numerical study is mainly performed for the one dimensional system case, addressing the issues of CPU cost, accuracy, non-oscillatory property, and resolution of discontinuities. Numerical tests are also performed for two dimensional systems.