Efficient Implementation of Weighted ENO Schemes

  title={Efficient Implementation of Weighted ENO Schemes},
  author={Guang-Shan Jiang and Chi-Wang Shu},
  journal={Journal of Computational Physics},
In this paper, we further analyze, test, modify, and improve the high order WENO (weighted essentially non-oscillatory) finite difference schemes of Liu, Osher, and Chan. It was shown by Liuet al.that WENO schemes constructed from therth order (inL1norm) ENO schemes are (r+ 1)th order accurate. We propose a new way of measuring the smoothness of a numerical solution, emulating the idea of minimizing the total variation of the approximation, which results in a fifth-order WENO scheme for the… 
Modified Stencil Approximations for Fifth-Order Weighted Essentially Non-oscillatory Schemes
In this paper, a modified fifth-order weighted essentially non-oscillatory (WENO) finite difference scheme is presented, modified by adding a form of cubic terms such that the resulting stencil approximation achieves fourth-order accuracy.
A simple algorithm to improve the performance of the WENO scheme on non-uniform grids
This paper presents a simple approach for improving the performance of the weighted essentially non-oscillatory (WENO) finite volume scheme on non-uniform grids. This technique relies on the
A novel method for constructing high accurate and robust WENO-Z type scheme
A novel method for constructing robust and high-order accurate weighted essentially non-oscillatory (WENO) scheme based on the WENO-Z type scheme, in which an eighth-order global smoothness indicator is used and the constant 1 used to calculate the un-normalized weights is replaced by a function of local smoothness indicators of candidate sub-stencils.
Improved Weight Functions of High-order WENO Schemes
It has been shown that the conventional 5th-order Weighted Essentially Non-Oscillatory (WENO) scheme of Jiang and Shu degenerates to third order at points where the first and higher order derivatives
An Improved Non-linear Weights for Seventh-Order WENO Scheme
The construction and implementation of a seventh order weighted essentially non-oscillatory scheme is reported for hyperbolic conservation laws and the scheme is implemented to non-linear scalar and system of equations in one and two dimensions.
High-Order ENO and WENO Schemes with Flux Gradient and Source Term Balancing
Results of extended numerical testing of the original ENO and WENO schemes and new schemes on one-dimensional shallow water equations and the time evolution of the numerical error due to variable bed depth in quiescent flow, steady state flow and unsteady flow are presented.


A new way of measuring the smoothness of a numerical solution is proposed, emulating the idea of minimizing the total variation of the approximation, which results in a 5th order WENO scheme for the case r=3, instead of the 4th order with the original smoothness measurement by Liu et al.
A numerical study of the convergence properties of ENO schemes
We report numerical results obtained with finite difference ENO schemes for the model problem of the linear convection equation with periodic boundary conditions. For the test function sin(x), the
91-1557, in AIAA 10th Computational Fluid 12
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