A modified high-order symmetrical WENO scheme for hyperbolic conservation laws
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Rooholah Abedian
Abstract
This paper designs a modified weighted essentially non-oscillatory (WENO) scheme for solving hyperbolic conservation laws. Using the switching principle based on inflection points, the new scheme automatically adapts between linear upwind and WENO schemes. If there is at least one inflection point in the largest stencil available for reconstruction, a symmetrical WENO (SWENO) scheme is considered for the reconstruction of the numerical flux; otherwise the numerical flux is directly approximated by the reconstruction polynomial. By comparing the new scheme introduced in this paper with the classical WENO scheme and another improved scheme that has been proposed recently D. Chai, G. Xi, Z. Sun, Z. Wangand Z. Huang,Comput. Fluids, vol. 170, pp. 176–186, 2018), we can point out the robustness and better efficiency of this scheme. To examine and explain the features of the new scheme, a number of examples such as Euler equations have been considered.
Acknowledgement
The author is very thankful to the reviewers for carefully reading the paper, their comments and suggestions have improved the quality of the paper.
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Author contribution: The author has accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: No funding was received for conducting this study.
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Conflict of interest statement: The author declares no conflicts of interest regarding this article.
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© 2022 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Original Research Articles
- Image-based 3D reconstruction precision using a camera mounted on a robot arm
- Switched-line network with digital phase shifter
- M-lump waves and their interactions with multi-soliton solutions for the (3 + 1)-dimensional Jimbo–Miwa equation
- Optimal control for a class of fractional order neutral evolution equations
- Perceptual evaluation for Zhangpu paper-cut patterns by using improved GWO-BP neural network
- Two new iterative schemes to approximate the fixed points for mappings
- Ulam’s type stability of impulsive delay integrodifferential equations in Banach spaces
- Generalization method of generating the continuous nested distributions
- Wellposedness of impulsive functional abstract second-order differential equations with state-dependent delay
- Numerical study of heat and mass transfer on the pulsatile flow of blood under atherosclerotic condition
- Dynamic propagation behaviors of pure mode I crack under stress wave loading by caustics
- Numerical simulation of buoyancy-induced heat transfer and entropy generation in 3D C-shaped cavity filled with CNT–Al2O3/water hybrid nanofluid
- On coupled system of nonlinear Ψ-Hilfer hybrid fractional differential equations
- Hellinger–Reissner variational principle for a class of specified stress problems
- Viscous dissipation effect on steady natural convection Couette flow with convective boundary condition
- Fredholm determinants and Z n -mKdV/Z n -sinh-Gordon hierarchies
- New soliton waves and modulation instability analysis for a metamaterials model via the integration schemes
- A modified high-order symmetrical WENO scheme for hyperbolic conservation laws
- Cryptanalysis of various images based on neural networks with leakage and time varying delays
- Spectral collocation method approach to thermal stability of MHD reactive squeezed fluid flow through a channel
- Higher order Traub–Steffensen type methods and their convergence analysis in Banach spaces
Artikel in diesem Heft
- Frontmatter
- Original Research Articles
- Image-based 3D reconstruction precision using a camera mounted on a robot arm
- Switched-line network with digital phase shifter
- M-lump waves and their interactions with multi-soliton solutions for the (3 + 1)-dimensional Jimbo–Miwa equation
- Optimal control for a class of fractional order neutral evolution equations
- Perceptual evaluation for Zhangpu paper-cut patterns by using improved GWO-BP neural network
- Two new iterative schemes to approximate the fixed points for mappings
- Ulam’s type stability of impulsive delay integrodifferential equations in Banach spaces
- Generalization method of generating the continuous nested distributions
- Wellposedness of impulsive functional abstract second-order differential equations with state-dependent delay
- Numerical study of heat and mass transfer on the pulsatile flow of blood under atherosclerotic condition
- Dynamic propagation behaviors of pure mode I crack under stress wave loading by caustics
- Numerical simulation of buoyancy-induced heat transfer and entropy generation in 3D C-shaped cavity filled with CNT–Al2O3/water hybrid nanofluid
- On coupled system of nonlinear Ψ-Hilfer hybrid fractional differential equations
- Hellinger–Reissner variational principle for a class of specified stress problems
- Viscous dissipation effect on steady natural convection Couette flow with convective boundary condition
- Fredholm determinants and Z n -mKdV/Z n -sinh-Gordon hierarchies
- New soliton waves and modulation instability analysis for a metamaterials model via the integration schemes
- A modified high-order symmetrical WENO scheme for hyperbolic conservation laws
- Cryptanalysis of various images based on neural networks with leakage and time varying delays
- Spectral collocation method approach to thermal stability of MHD reactive squeezed fluid flow through a channel
- Higher order Traub–Steffensen type methods and their convergence analysis in Banach spaces
