Towards a compact high-order method for non-linear hyperbolic systems. I: The Hermite least-square monotone (HLSM) reconstruction

DOI10.1016/j.jcp.2009.02.005zbMath1166.65375OpenAlexW1967981428MaRDI QIDQ1025134

Guy Capdeville

Publication date: 18 June 2009

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

Full work available at URL: https://doi.org/10.1016/j.jcp.2009.02.005

zbMATH Keywords

finite volume methodnumerical experimentshyperbolic systemsmethod of linesHermite polynomialnon-uniform meshesaero-acousticsupwind discretizationleast-square reconstructiondata-depending weightmulti-scales problems

Mathematics Subject Classification ID

Finite volume methods applied to problems in fluid mechanics (76M12) Hyperbolic conservation laws (35L65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Hydro- and aero-acoustics (76Q05) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

Related Items (4)

Hermite upwind positive schemes (HUPS) for non-linear hyperbolic systems of conservation laws ⋮ High-order solution-adaptive central essentially non-oscillatory (CENO) method for viscous flows ⋮ Towards a compact high-order method for non-linear hyperbolic systems. II: The Hermite-HLLC scheme ⋮ Compact high-order numerical schemes for scalar hyperbolic partial differential equations

Cites Work

• The Riemann problem admitting \(\delta-, \delta ^{\prime }\)-shocks, and vacuum states (the vanishing viscosity approach)
• CIP/multi-moment finite volume method for Euler equations: A semi-Lagrangian characteristic formulation
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• On the construction, comparison, and local characteristic decomposition for high-order central WENO schemes
• A Hermite upwind WENO scheme for solving hyperbolic conservation laws
• Central schemes on overlapping cells
• Numerical Computations of Turbulence Amplification in Shock-Wave Interactions
• Interaction of Linear Waves with Oblique Shock Waves

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