Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Total variation diminishing Runge-Kutta schemes
Mathematics of Computation
A technique of treating negative weights in WENO schemes
Journal of Computational Physics
High-Order WENO Schemes for Hamilton-Jacobi Equations on Triangular Meshes
SIAM Journal on Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
High-Order Central WENO Schemes for Multidimensional Hamilton--Jacobi Equations
SIAM Journal on Numerical Analysis
WENO schemes for balance laws with spatially varying flux
Journal of Computational Physics
Journal of Computational Physics
Mapped weighted essentially non-oscillatory schemes: Achieving optimal order near critical points
Journal of Computational Physics
A Weighted Essentially Nonoscillatory, Large Time-Step Scheme for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
Journal of Scientific Computing
A Fifth Order Flux Implicit WENO Method
Journal of Scientific Computing
Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows
Journal of Computational Physics
An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws
Journal of Computational Physics
Strong stability of singly-diagonally-implicit Runge--Kutta methods
Applied Numerical Mathematics
High Order Strong Stability Preserving Time Discretizations
Journal of Scientific Computing
Journal of Computational Physics
Some results on uniformly high-order accurate essentially nonoscillatory schemes
Applied Numerical Mathematics
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
Journal of Computational Physics
Hi-index | 7.29 |
Weighted essentially non-oscillatory (WENO) schemes have been mainly used for solving hyperbolic partial differential equations (PDEs). Such schemes are capable of high order approximation in smooth regions and non-oscillatory sharp resolution of discontinuities. The base of the WENO schemes is a non-oscillatory WENO approximation procedure, which is not necessarily related to PDEs. The typical WENO procedures are WENO interpolation and WENO reconstruction. The WENO algorithm has gained much popularity but the basic idea of approximation did not change much over the years. In this paper, we first briefly review the idea of WENO interpolation and propose a modification of the basic algorithm. New approximation should improve basic characteristics of the approximation and provide a more flexible framework for future applications. New WENO procedure involves a binary tree weighted construction that is based on key ideas of WENO algorithm and we refer to it as the binary weighted essentially non-oscillatory (BWENO) approximation. New algorithm comes in a rational and a polynomial version. Furthermore, we describe the WENO reconstruction procedure, which is usually involved in the numerical schemes for hyperbolic PDEs, and propose the new reconstruction procedure based on the described BWENO interpolation. The obtained numerical results show that the newly proposed procedures perform very well on the considered test examples.