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
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
Journal of Computational Physics
Numerical experiments on the accuracy of ENO and modified ENO schemes
Journal of Scientific Computing
A numerical study of the convergence properties of ENO schemes
Journal of Scientific Computing
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
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
Solution of Two-Dimensional Riemann Problems of Gas Dynamics by Positive Schemes
SIAM Journal on Scientific Computing
Weighted essentially non-oscillatory schemes on triangular meshes
Journal of Computational Physics
A problem-independent limiter for high-order Runge—Kutta discontinuous Galerkin methods
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
A Hermite WENO-based limiter for discontinuous Galerkin method on unstructured grids
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Runge-Kutta discontinuous Galerkin method using WENO limiters II: Unstructured meshes
Journal of Computational Physics
Hierarchical reconstruction for spectral volume method on unstructured grids
Journal of Computational Physics
Journal of Computational Physics
Self-adjusting, positivity preserving high order schemes for hydrodynamics and magnetohydrodynamics
Journal of Computational Physics
An adaptive finite volume method for 2D steady Euler equations with WENO reconstruction
Journal of Computational Physics
WENO schemes on arbitrary unstructured meshes for laminar, transitional and turbulent flows
Journal of Computational Physics
High-order solution-adaptive central essentially non-oscillatory (CENO) method for viscous flows
Journal of Computational Physics
Hi-index | 31.49 |
The hierarchical reconstruction (HR) [Y.-J. Liu, C.-W. Shu, E. Tadmor, M.-P. Zhang, Central discontinuous Galerkin methods on overlapping cells with a non-oscillatory hierarchical reconstruction, SIAM J. Numer. Anal. 45 (2007) 2442-2467] is applied to the piecewise quadratic discontinuous Galerkin method on two-dimensional unstructured triangular grids. A variety of limiter functions have been explored in the construction of piecewise linear polynomials in every hierarchical reconstruction stage. We show that on triangular grids, the use of center biased limiter functions is essential in order to recover the desired order of accuracy. Several new techniques have been developed in the paper: (a) we develop a WENO-type linear reconstruction in each hierarchical level, which solves the accuracy degeneracy problem of previous limiter functions and is essentially independent of the local mesh structure; (b) we find that HR using partial neighboring cells significantly reduces over/under-shoots, and further improves the resolution of the numerical solutions. The method is compact and therefore easy to implement. Numerical computations for scalar and systems of nonlinear hyperbolic equations are performed. We demonstrate that the procedure can generate essentially non-oscillatory solutions while keeping the resolution and desired order of accuracy for smooth solutions.