Natural continuous extensions of Runge-Kutta formulas
Mathematics of Computation
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
Non-oscillatory central differencing for hyperbolic conservation laws
Journal of Computational Physics
Numerical experiments on the accuracy of ENO and modified ENO schemes
Journal of Scientific Computing
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Journal of Computational Physics
Nonoscillatory Central Schemes for Multidimensional Hyperbolic Conservation Laws
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
Weighted essentially non-oscillatory schemes on triangular meshes
Journal of Computational Physics
High-Order Central Schemes for Hyperbolic Systems of Conservation Laws
SIAM Journal on Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
On the behavior of the total variation in CWENO methods for conservation laws
Proceedings of the fourth international conference on Spectral and high order methods (ICOSAHOM 1998)
A third order central WENO scheme for 2D conservation laws
Proceedings of the fourth international conference on Spectral and high order methods (ICOSAHOM 1998)
A technique of treating negative weights in WENO schemes
Journal of Computational Physics
A Third-Order Semidiscrete Central Scheme for Conservation Laws and Convection-Diffusion Equations
SIAM Journal on Scientific Computing
Compact Central WENO Schemes for Multidimensional Conservation Laws
SIAM Journal on Scientific Computing
Semidiscrete Central-Upwind Schemes for Hyperbolic Conservation Laws and Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
Journal of Computational Physics
Relaxed High Resolution Schemes for Hyperbolic Conservation Laws
Journal of Scientific Computing
Journal of Computational Physics
Hermite WENO schemes for Hamilton-Jacobi equations
Journal of Computational Physics
Central schemes on overlapping cells
Journal of Computational Physics
Implicit---Explicit Runge---Kutta Schemes and Applications to Hyperbolic Systems with Relaxation
Journal of Scientific Computing
Staggered Finite Difference Schemes for Conservation Laws
Journal of Scientific Computing
On the Total Variation of High-Order Semi-Discrete Central Schemes for Conservation Laws
Journal of Scientific Computing
A windowed Fourier pseudospectral method for hyperbolic conservation laws
Journal of Computational Physics
Numerical simulation of Camassa-Holm peakons by adaptive upwinding
Applied Numerical Mathematics
Fourth-order balanced source term treatment in central WENO schemes for shallow water equations
Journal of Computational Physics
Implementation of WENO schemes in compressible multicomponent flow problems
Journal of Computational Physics
δ-mapping algorithm coupled with WENO reconstruction for nonlinear elasticity in heterogeneous media
Applied Numerical Mathematics
A Hermite upwind WENO scheme for solving hyperbolic conservation laws
Journal of Computational Physics
A central WENO scheme for solving hyperbolic conservation laws on non-uniform meshes
Journal of Computational Physics
Runge-Kutta discontinuous Galerkin method using WENO limiters II: Unstructured meshes
Journal of Computational Physics
A new fourth-order non-oscillatory central scheme for hyperbolic conservation laws
Applied Numerical Mathematics
Multi-dimensional limiting process for three-dimensional flow physics analyses
Journal of Computational Physics
Journal of Computational Physics
Non-oscillatory central-upwind scheme for hyperbolic conservation laws
International Journal of Computational Fluid Dynamics
Finite volume and WENO scheme in one-dimensional vascular system modelling
Computers & Mathematics with Applications
Third-order Energy Stable WENO scheme
Journal of Computational Physics
Journal of Computational Physics
Journal of Scientific Computing
Exact and approximate solutions of Riemann problems in non-linear elasticity
Journal of Computational Physics
Numerical simulation of Camassa--Holm peakons by adaptive upwinding
Applied Numerical Mathematics
Approximation error of the Lagrange reconstructing polynomial
Journal of Approximation Theory
Relaxation method for unsteady convection-diffusion equations
Computers & Mathematics with Applications
A high-order multi-dimensional HLL-Riemann solver for non-linear Euler equations
Journal of Computational Physics
Journal of Computational Physics
Binary weighted essentially non-oscillatory (BWENO) approximation
Journal of Computational and Applied Mathematics
Representation of the Lagrange reconstructing polynomial by combination of substencils
Journal of Computational and Applied Mathematics
An Eulerian-Lagrangian WENO finite volume scheme for advection problems
Journal of Computational Physics
A simple weighted essentially nonoscillatory limiter for Runge-Kutta discontinuous Galerkin methods
Journal of Computational Physics
Journal of Scientific Computing
A HLL-Rankine-Hugoniot Riemann solver for complex non-linear hyperbolic problems
Journal of Computational Physics
Journal of Scientific Computing
A re-averaged WENO reconstruction and a third order CWENO scheme for hyperbolic conservation laws
Journal of Computational Physics
Hi-index | 31.55 |
In this paper, we review and construct fifth- and ninth-order central weighted essentially nonoscillatory (WENO) schemes based on a finite volume formulation, staggered mesh, and continuous extension of Runge-Kutta methods for solving non-linear hyperbolic conservation law systems. Negative linear weights appear in such a formulation and they are treated using the technique recently introduced by Shi et al. (J. Comput. Phys. 175, 108 (2002)). We then perform numerical computations and comparisons with the finite difference WENO schemes of Jiang and Shu (J. Comput. Phys. 150, 97 (1999)) and Balsara and Shu (J. Comput. Phys. 160, 405 (2000)). The emphasis is on the performance with or without a local characteristic decomposition. While this decomposition increases the computational cost, we demonstrate by our numerical experiments that it is still necessary to use it to control spurious oscillations when the order of accuracy is high, both for the central staggered grid and for the upwind nonstaggered grid WENO schemes. We use the shock entropy wave interaction problem to demonstrate the advantage of using higher order WENO schemes when both shocks and complex solution features coexist.