Improvement of third-order WENO-Z scheme at critical points

DOI10.1016/j.camwa.2018.02.009zbMath1409.65060OpenAlexW2790912969MaRDI QIDQ1732557

Wei-guo Wu, Wei-zheng Xu

Publication date: 25 March 2019

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2018.02.009

zbMATH Keywords

Euler equationshyperbolic conservation lawsWENO schemessmoothness indicatornonlinear weightshigh-resolution

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12)

Related Items (12)

Improvement of third-order finite difference WENO scheme at critical points ⋮ Improving the third-order WENO schemes by using exponential polynomial space with a locally optimized shape parameter ⋮ A New Third-Order Finite Difference WENO Scheme to Improve Convergence Rate at Critical Points ⋮ A smoothness indicators free third-order weighted ENO scheme for gas-dynamic Euler equations ⋮ Fifth-order weighted essentially non-oscillatory schemes with new Z-type nonlinear weights for hyperbolic conservation laws ⋮ A New Fifth-Order Finite Difference WENO Scheme for Dam-Break Simulations ⋮ A modified seventh-order WENO scheme with new nonlinear weights for hyperbolic conservation laws ⋮ A third-order WENO scheme based on exponential polynomials for Hamilton-Jacobi equations ⋮ Modified third and fifth order WENO schemes for inviscid compressible flows ⋮ An improvement of third order WENO scheme for convergence rate at critical points with new non-linear weights ⋮ Third-order scale-independent WENO-Z scheme to achieve optimal order at critical points ⋮ Development of a Modified Seventh-Order WENO Scheme with New Nonlinear Weights

Cites Work

• Modified non-linear weights for fifth-order weighted essentially non-oscillatory schemes
• Accuracy of the weighted essentially non-oscillatory conservative finite difference schemes
• A new smoothness indicator for improving the weighted essentially non-oscillatory scheme
• High order weighted essentially nonoscillatory WENO-\(\eta\) schemes for hyperbolic conservation laws
• High order weighted essentially non-oscillatory WENO-Z schemes for hyperbolic conservation laws
• Finite-volume WENO schemes for three-dimensional conservation laws
• Third-order energy stable WENO scheme
• The numerical simulation of two-dimensional fluid flow with strong shocks
• Efficient implementation of essentially nonoscillatory shock-capturing schemes
• Weighted essentially non-oscillatory schemes
• Improvement of weighted essentially non-oscillatory schemes near discontinuities
• An efficient adaptive high-order scheme based on the WENO process
• Mapped weighted essentially non-oscillatory schemes: Achieving optimal order near critical points
• Resolution of high order WENO schemes for complicated flow structures.
• Efficient implementation of weighted ENO schemes
• An improved weighted essentially non-oscillatory scheme with a new smoothness indicator
• An improved WENO-Z scheme
• An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws
• Solution of Two-Dimensional Riemann Problems of Gas Dynamics by Positive Schemes

This page was built for publication: Improvement of third-order WENO-Z scheme at critical points