Total-variation-diminishing time discretizations
SIAM Journal on Scientific and Statistical Computing
Journal of Computational Physics
New algorithms for ultra-relativistic numerical hydrodynamics
Journal of Computational Physics
Parallel, adaptive finite element methods for conservation laws
Proceedings of the third ARO workshop on Adaptive methods for partial differential equations
Relativistic hydrodynamics and essentially non-oscillatory shock capturing schemes
Journal of Computational Physics
Extension of the piecewise parabolic method to one-dimensional relativistic hydrodynamics
Journal of Computational Physics
An Iterative Riemann Solver for Relativistic Hydrodynamics
SIAM Journal on Scientific Computing
A kinetic beam scheme for relativistic gas dynamics
Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
A flux-split algorithm applied to relativistic flows
Journal of Computational Physics
A problem-independent limiter for high-order Runge—Kutta discontinuous Galerkin methods
Journal of Computational Physics
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Kinetic schemes for the relativistic gas dynamics
Numerische Mathematik
Runge--Kutta Discontinuous Galerkin Method Using WENO Limiters
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Runge-Kutta discontinuous Galerkin method using WENO limiters II: Unstructured meshes
Journal of Computational Physics
Riemann Solver for Relativistic Hydrodynamics
Journal of Computational Physics
A high-order kinetic flux-splitting method for the relativistic magnetohydrodynamics
Journal of Computational Physics
A direct Eulerian GRP scheme for relativistic hydrodynamics: One-dimensional case
Journal of Computational Physics
A direct Eulerian GRP scheme for relativistic hydrodynamics: Two-dimensional case
Journal of Computational Physics
A simple weighted essentially nonoscillatory limiter for Runge-Kutta discontinuous Galerkin methods
Journal of Computational Physics
Finite volume local evolution Galerkin method for two-dimensional relativistic hydrodynamics
Journal of Computational Physics
A third-order accurate direct Eulerian GRP scheme for the Euler equations in gas dynamics
Journal of Computational Physics
Hi-index | 31.46 |
This paper develops the P^K-based Runge-Kutta discontinuous Galerkin (RKDG) methods with WENO limiter for the one- and two-dimensional special relativistic hydrodynamics, K=1,2,3, which is an extension of the work [J.X. Qiu, C.-W. Shu, Runge-Kutta discontinuous Galerkin method using WENO limiters, SIAM J. Sci. Comput. 26 (2005) 907-929]. The WENO limiter for the RKDG method is adaptively implemented via two following steps: the ''troubled'' cells are first identified by using a TVB modified minmod function, and then a new polynomial solution inside the ''troubled'' cells is locally reconstructed to replace the RKDG solution by using the WENO technique based on the cell average values of the RKDG solution in the neighboring cells as well as the original cell averages of the ''troubled'' cells. Several test problems in one and two dimensions are computed using the developed RKDG methods with WENO limiter. The computations demonstrate that our methods are stable, accurate, and robust in maintaining accuracy for simulating flows in the special relativistic hydrodynamics.