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Primitive upwind numerical methods for hyperbolic partial differential equations

  • E. F. Toro
  • R. C. Millington
  • L. A. M. Nejad
Schemes And Methods Analysis Communications
Part of the Lecture Notes in Physics book series (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)].

Key Words

Hyperbolic PDEs Primitive Schemes Riemann Solvers Godunov Method 

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References

  1. Ben-Artzi M. and Falcovitz J., A Second Order Godunov-Type Scheme for Compressible Fluid Dynamics. J. Comput. Phys., 55:1–32, 1984.MATHCrossRefADSMathSciNetGoogle Scholar
  2. Hirsch C., Numerical Computation of Internal and External Flows, Vol. II: Computational Methods for Inviscid and Viscous Flows. Wiley, 1990Google Scholar
  3. Millington R. C, Toro E. F. and Nejad L. A. M., Arbitrary high order numerical methods for hyperbolic systems with constant coefficients. In preparation., 1998Google Scholar
  4. Toro E. F., Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer-Verlag, 1997Google Scholar
  5. 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.Google Scholar

Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • E. F. Toro
    • 1
  • R. C. Millington
    • 1
  • L. A. M. Nejad
    • 1
  1. 1.Department of Computing and MathematicsManchester Metropolitan UniversityManchesterUK

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