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
Parallel, adaptive finite element methods for conservation laws
Proceedings of the third ARO workshop on Adaptive methods for partial differential equations
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Approximate Riemann solvers, parameter vectors, and difference schemes
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
Journal of Computational Physics
Weighted essentially non-oscillatory schemes on triangular meshes
Journal of Computational Physics
Journal of Computational Physics
A problem-independent limiter for high-order Runge—Kutta discontinuous Galerkin methods
Journal of Computational Physics
A technique of treating negative weights in WENO schemes
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Runge--Kutta Discontinuous Galerkin Method Using WENO Limiters
SIAM Journal on Scientific Computing
ADER schemes on adaptive triangular meshes for scalar conservation laws
Journal of Computational Physics
SIAM Journal on Scientific Computing
Journal of Computational Physics
Runge-Kutta discontinuous Galerkin method using WENO limiters II: Unstructured meshes
Journal of Computational Physics
High Order Strong Stability Preserving Time Discretizations
Journal of Scientific Computing
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
Journal of Computational Physics
Robust high order discontinuous Galerkin schemes for two-dimensional gaseous detonations
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.45 |
In this paper, we investigate a simple limiter using weighted essentially non-oscillatory (WENO) methodology for the Runge-Kutta discontinuous Galerkin (RKDG) methods solving conservation laws, with the goal of obtaining a robust and high order limiting procedure to simultaneously achieve uniform high order accuracy and sharp, non-oscillatory shock transitions. The idea of this limiter is to reconstruct the entire polynomial, instead of reconstructing point values or moments in the classical WENO reconstructions. That is, the reconstruction polynomial on the target cell is a convex combination of polynomials on this cell and its neighboring cells and the nonlinear weights of the convex combination follow the classical WENO procedure. The main advantage of this limiter is its simplicity in implementation, especially for multi-dimensional meshes. Numerical results in one and two dimensions are provided to illustrate the behavior of this procedure.