Geometric interpretations and spatial symmetry property of metrics in the conservative form for high-order finite-difference schemes on moving and deforming grids

DOI10.1016/J.JCP.2013.12.019zbMath1349.65552OpenAlexW2089804626WikidataQ61663214 ScholiaQ61663214MaRDI QIDQ348775

Yoshiaki Abe, Kozo Fujii, Taku Nonomura, Nobuyuki Iizuka

Publication date: 5 December 2016

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

Full work available at URL: https://doi.org/10.1016/j.jcp.2013.12.019

zbMATH Keywords

high-order schemecommutativitygeometric conservation lawmoving and deforming gridsbody-fitted coordinateconservative metricfreestream preservationgeometric interpretation

Mathematics Subject Classification ID

Finite difference methods for boundary value problems involving PDEs (65N06) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

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Cites Work

• Unnamed Item
• Freestream and vortex preservation properties of high-order WENO and WCNS on curvilinear grids
• Geometric conservation law and applications to high-order finite difference schemes with stationary grids
• A multi-dimensional upwind scheme for the Euler equations on structured grids
• Skew-symmetric convection form and secondary conservative finite difference methods for moving grids
• ADI-SGS scheme on ideal magnetohydrodynamics
• An analysis of finite-difference and finite-volume formulations of conservation laws
• Boundary-fitted coordinate systems for numerical solution of partial differential equations. A review
• Compact finite difference schemes with spectral-like resolution
• Fully conservative higher order finite difference schemes for incompressible flow
• Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy
• Discrete form of the GCL for moving meshes and its implementation in CFD schemes
• On the use of higher-order finite-difference schemes on curvilinear and deforming meshes
• Further studies on geometric conservation law and applications to high-order finite difference schemes with stationary grids
• Geometric Conservation Law and Its Application to Flow Computations on Moving Grids
• Calculation of plane steady transonic flows

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