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Sixteenth International Conference on Numerical Methods in Fluid Dynamics pp 421–426Cite as

Primitive upwind numerical methods for hyperbolic partial differential equations

  • Schemes And Methods Analysis
  • Conference paper
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Part of the book series: Lecture Notes in Physics ((LNP,volume 515))

Abstract

This paper is about the construction of numerical methods based on non-conservative formulations of hyperbolic PDEs. The methods are explicit and Riemann-problem based upwind. Schemes of first, second and higher order of accuracy are constructed. A modified grp approach leads to arbitrarily high order schemes, in which sequences of Riemann problems for high-order spatial gradients are solved. Other approaches and related issues are presented in detail in [Toro (97)], [Toro (98)].

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References

  • Ben-Artzi M. and Falcovitz J., A Second Order Godunov-Type Scheme for Compressible Fluid Dynamics. J. Comput. Phys., 55:1–32, 1984.

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  • Millington R. C, Toro E. F. and Nejad L. A. M., Arbitrary high order numerical methods for hyperbolic systems with constant coefficients. In preparation., 1998

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  • Toro E. F., Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer-Verlag, 1997

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  • Toro E. F., Primitive, Conservative and Adaptive Schemes for Hyperbolic Conservation Laws. Numerical Methods for Wave Propagation Problems. With the Harten Memorial Lecture, by P. L. Roe. (Editors: Toro, E. F. and Clarke, J. F.), Kluwer Academic Publishers, 1998.

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Author information

Authors and Affiliations

  1. Department of Computing and Mathematics, Manchester Metropolitan University, Chester Street, M1 5GD, Manchester, UK

    E. F. Toro, R. C. Millington & L. A. M. Nejad

Authors
  1. E. F. Toro
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  2. R. C. Millington
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  3. L. A. M. Nejad
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Editor information

Charles-Henri Bruneau

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© 1998 Springer-Verlag

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Toro, E.F., Millington, R.C., Nejad, L.A.M. (1998). Primitive upwind numerical methods for hyperbolic partial differential equations. In: Bruneau, CH. (eds) Sixteenth International Conference on Numerical Methods in Fluid Dynamics. Lecture Notes in Physics, vol 515. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0106618

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  • DOI: https://doi.org/10.1007/BFb0106618

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65153-6

  • Online ISBN: 978-3-540-49540-6

  • eBook Packages: Springer Book Archive

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