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Proceedings of the Third GAMM — Conference on Numerical Methods in Fluid Mechanics pp 211–220Cite as

A Fourth-Order Compact Implicit Scheme for Solving the Non-Linear Shallow-Water Equations in Conservation-Law Form

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Part of the book series: Notes on Numerical Fluid Mechanics ((NNFM,volume 2))

Summary

A Fourth-order compact implicit finite-difference scheme is applied for solving numerically the nonlinear shallow-water equations in conservation-law form. The algorithm is second-order time accurate, while fourth-order compact differencing is implemented in a spatially factored (ADI) form. Third-order uncentered boundary conditions which preserve the overall fourth-order convergence are experimented with and compared. Von Neuman linearized stability analysis as well as Kreiss-type normal-mode analysis are performed. The integral invariants of the shallow-water equations are well conserved during the numerical integration. Accuracy tests confirm the fourth-order accuracy of the scheme.

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Authors and Affiliations

  1. National Research Institute for Mathematical Sciences, CSIR, Pretoria, South Africa

    I. M. Navon

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  1. I. M. Navon
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Editors and Affiliations

  1. DFVLR-Institut für Theoretische Störungsmechanik, Linder Höhe, 5000, Köln 90, Fed. Rep. of Germany

    E. H. Hirschel (Chairman) (Chairman)

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© 1980 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig

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Navon, I.M. (1980). A Fourth-Order Compact Implicit Scheme for Solving the Non-Linear Shallow-Water Equations in Conservation-Law Form. In: Hirschel, E.H. (eds) Proceedings of the Third GAMM — Conference on Numerical Methods in Fluid Mechanics. Notes on Numerical Fluid Mechanics, vol 2. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-322-86146-7_22

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  • DOI: https://doi.org/10.1007/978-3-322-86146-7_22

  • Publisher Name: Vieweg+Teubner Verlag, Wiesbaden

  • Print ISBN: 978-3-528-08076-1

  • Online ISBN: 978-3-322-86146-7

  • eBook Packages: Springer Book Archive

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