A stable and conservative method for locally adapting the design order of finite difference schemes

DOI10.1016/j.jcp.2010.11.020zbMath1220.65112OpenAlexW2071372263MaRDI QIDQ550859

Qaisar Abbas, Sofia Eriksson, Jan Nordström

Publication date: 13 July 2011

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-67055

zbMATH Keywords

stabilitynumerical experimentsBurgers equationfinite difference methodsadvection equationconservationhigh order accuracysummation-by-partsmonotone upwind schemes for conservation laws (MUSCL) techniqueshock calculations

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) KdV equations (Korteweg-de Vries equations) (35Q53) 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) Initial value problems for first-order hyperbolic systems (35L45)

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Cites Work

• Unnamed Item
• Unnamed Item
• On the order of accuracy for difference approximations of initial-boundary value problems
• A stable high-order finite difference scheme for the compressible Navier-Stokes equations: No-slip wall boundary conditions
• Stable and accurate wave-propagation in discontinuous media
• A stable and conservative high order multi-block method for the compressible Navier-Stokes equations
• Uniformly high order accurate essentially non-oscillatory schemes. III
• Efficient implementation of essentially nonoscillatory shock-capturing schemes. II
• A stable and conservative interface treatment of arbitrary spatial accuracy
• Summation by parts for finite difference approximations for \(d/dx\)
• Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes
• High order finite difference approximations of electromagnetic wave propagation close to material discontinuities
• Hybrid tuned center-difference-WENO method for large eddy simulations in the presence of strong shocks.
• Summation by parts operators for finite difference approximations of second derivatives
• Efficient implementation of weighted ENO schemes
• Strict stability of high-order compact implicit finite-difference schemes: The role of boundary conditions for hyperbolic PDEs. I
• Analysis of the order of accuracy for node-centered finite volume schemes
• Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
• A stable high-order finite difference scheme for the compressible Navier-Stokes equations, far-field boundary conditions
• Stability criteria for hybrid difference methods
• A stable hybrid method for hyperbolic problems
• Stability Theory of Difference Approximations for Mixed Initial Boundary Value Problems. II