Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
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
Numerical solution of the Riemann problem for two-dimensional gas dynamics
SIAM Journal on Scientific Computing
Local piecewise hyperbolic reconstruction of numerical fluxes for nonlinear scalar conservation laws
SIAM Journal on Scientific Computing
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Capturing shock reflections: an improved flux formula
Journal of Computational Physics
Moving mesh methods with upwinding schemes for time-dependent PDEs
Journal of Computational Physics
Applied Numerical Mathematics - Numerical methods for viscosity solutions and applications
Journal of Scientific Computing
A new fourth-order non-oscillatory central scheme for hyperbolic conservation laws
Applied Numerical Mathematics
Point values Hermite multiresolution for non-smooth noisy signals II
ISPRA'06 Proceedings of the 5th WSEAS International Conference on Signal Processing, Robotics and Automation
Journal of Computational Physics
High order weighted essentially non-oscillatory WENO-Z schemes for hyperbolic conservation laws
Journal of Computational Physics
Analysis of a class of nonlinear subdivision schemes and associated multiresolution transforms
Advances in Computational Mathematics
Improvement of Convergence to Steady State Solutions of Euler Equations with the WENO Schemes
Journal of Scientific Computing
Weighted-powerp nonlinear subdivision schemes
Proceedings of the 7th international conference on Curves and Surfaces
Analysis of a class of nonlinear and non-separable multiscale representations
Numerical Algorithms
A class of nonlinear four-point subdivision schemes
Advances in Computational Mathematics
New adaptive artificial viscosity method for hyperbolic systems of conservation laws
Journal of Computational Physics
An improved weighted essentially non-oscillatory scheme with a new smoothness indicator
Journal of Computational Physics
A Robust Reconstruction for Unstructured WENO Schemes
Journal of Scientific Computing
High order nonlinear interpolatory reconstruction operators and associated multiresolution schemes
Journal of Computational and Applied Mathematics
Applied Numerical Mathematics
Hi-index | 31.47 |
In this paper we introduce a new class of ENO reconstruction procedures, the Power ENO methods, to design high-order accurate shock capturing methods for hyperbolic conservation laws, based on an extended class of limiters, improving the behavior near discontinuities with respect to the classical ENO methods. Power ENO methods are defined as a correction of classical ENO methods [J. Comput. Phys. 71 (1987) 231], by applying the new limiters on second-order differences or higher. The new class of limiters includes as a particular case the minmod limiter and the harmonic limiter used for the design of the PHM methods [see SIAM J. Sci. Comput. 15 (1994) 892]. The main features of these new ENO methods are the substantially reduced smearing near discontinuities and the good resolution of corners and local extrema. We design a new fifth-order accurate Weighted Power ENO method that improves the behavior of Jiang-Shu WENO5 [J. Comput. Phys. 126 (1996) 202]. We present several one- and two-dimensional numerical experiments for scalar and systems of conservation laws, including linear advections and one- and two-dimensional Riemann problems for the Euler equations of gas dynamics, comparing our methods with the classical and weighted ENO methods, showing the advantages and disadvantages.