Nonlinear Comparison of High-order and Optimized Finite-difference Schemes

DOI10.1080/10618560008940902zbMath0964.76063OpenAlexW1995761977MaRDI QIDQ4503161

Ray Hixon

Publication date: 16 July 2001

Published in: International Journal of Computational Fluid Dynamics (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/2060/19990008949

zbMATH Keywords

optimizationfinite difference schemecompact schemenonlinear wave propagationexplicit schemeabsolute error\(L(2)\) errorone-dimensional nonlinear unsteady inviscid Burgers equation

Mathematics Subject Classification ID

Finite difference methods applied to problems in fluid mechanics (76M20) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06)

Related Items (9)

Implicit eighth-order central compact scheme for the numerical simulation of steady and unsteady incompressible Navier–Stokes equations ⋮ New optimized fourth-order compact finite difference schemes for wave propagation phenomena ⋮ A dispersively accurate compact finite difference method for the Degasperis-Procesi equation ⋮ Construction of explicit and implicit dynamic finite difference schemes and application to the large eddy simulation of the Taylor-Green vortex ⋮ A family of dynamic finite difference schemes for large eddy simulation ⋮ A new time-space domain high-order finite-difference method for the acoustic wave equation ⋮ Solution of unsteady Euler equations: gust-cascade interaction tones ⋮ Holberg's optimisation for high-order compact finite difference staggered schemes ⋮ A high-order accurate method for two-dimensional incompressible viscous flows

Cites Work

• Unnamed Item
• Dispersion-relation-preserving finite differene schemes for computational acoustics
• Uniformly high order accurate essentially non-oscillatory schemes. III
• Compact finite difference schemes with spectral-like resolution
• \(2N\)-storage low dissipation and dispersion Runge-Kutta schemes for computational acoustics
• Several new numerical methods for compressible shear-layer simulations
• Stable and accurate boundary treatments for compact, high-order finite- difference schemes

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