On the positivity of linear weights in WENO approximations

DOI10.1007/s10255-008-8826-yzbMath1177.65126OpenAlexW2035328844MaRDI QIDQ1036930

J. Blot

Publication date: 13 November 2009

Published in: Acta Mathematicae Applicatae Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10255-008-8826-y

zbMATH Keywords

numerical exampleshyperbolic partial differential equationsWENO reconstructionWENO interpolationweighted essentially non-oscillatory (WENO) schemeWENO integrationWENO approximation to derivatives

Mathematics Subject Classification ID

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

Related Items (19)

Essentially non-oscillatory and weighted essentially non-oscillatory schemes ⋮ Conservative semi-Lagrangian schemes for kinetic equations. I: Reconstruction ⋮ A re-averaged WENO reconstruction and a third order CWENO scheme for hyperbolic conservation laws ⋮ Positivity-preserving high order finite difference WENO schemes for compressible Navier-Stokes equations ⋮ Energy balanced numerical schemes with very high order. The augmented Roe flux ADER scheme. Application to the shallow water equations ⋮ A WENO-based method of lines transpose approach for Vlasov simulations ⋮ Evaluation of finite difference based asynchronous partial differential equations solver for reacting flows ⋮ Approximation error of the Lagrange reconstructing polynomial ⋮ A high-order semi-Lagrangian finite difference method for nonlinear Vlasov and BGK models ⋮ An Eulerian-Lagrangian WENO finite volume scheme for advection problems ⋮ Parametrized maximum principle preserving flux limiters for high order schemes solving multi-dimensional scalar hyperbolic conservation laws ⋮ A truly forward semi-Lagrangian WENO scheme for the Vlasov-Poisson system ⋮ WENO interpolation for Lagrangian particles in highly compressible flow regimes ⋮ Improvement of convergence to steady state solutions of Euler equations with the WENO Schemes ⋮ Fast sparse grid simulations of fifth order WENO scheme for high dimensional hyperbolic PDEs ⋮ High order finite difference multi-resolution WENO method for nonlinear degenerate parabolic equations ⋮ Kernel based high order ``explicit unconditionally stable scheme for nonlinear degenerate advection-diffusion equations ⋮ Binary weighted essentially non-oscillatory (BWENO) approximation ⋮ A general recurrence relation for the weight-functions in Mühlbach-Neville-Aitken representations with application to WENO interpolation and differentiation

Cites Work

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• High order residual distribution conservative finite difference WENO schemes for convection-diffusion steady state problems on non-smooth meshes
• Uniformly high order accurate essentially non-oscillatory schemes. III
• Weighted essentially non-oscillatory schemes
• Multidomain WENO finite difference method with interpolation at subdomain interfaces
• Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy
• Efficient implementation of weighted ENO schemes
• High order residual distribution conservative finite difference WENO schemes for steady state problems on nonsmooth meshes
• High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems
• A Weighted Essentially Nonoscillatory, Large Time-Step Scheme for Hamilton--Jacobi Equations
• A technique of treating negative weights in WENO schemes

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