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Journal of Engineering Mathematics

, Volume 23, Issue 1, pp 17–28 | Cite as

Flux difference splitting for the Euler equations in generalised coordinates using a local parameterisation of the equation of state

  • P. Glaister
Article
  • 42 Downloads

Abstract

An efficient algorithm based on flux difference splitting is presented for the solution of the three-dimensional Euler equations of gas dynamics in a generalised coordinate system with a general equation of state. The scheme is based on solving linearised Riemann problems approximately and in more than one dimension incorporates operator splitting. The algorithm uses a local parameterisation of the equation of state and as a consequence requires only one function evaluation in each computational cell. The scheme has good shock capturing properties and the advantage of using body-fitted meshes. Numerical results are shown for Mach 8 flow of “equilibrium air” past a circular cylinder.

Keywords

Mathematical Modeling Coordinate System Function Evaluation Industrial Mathematic Euler Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    P.L. Roe, Approximate Riemann solvers, parameters vectors and difference schemes, J. Comput. Phys. 49 (1983) 357–372.Google Scholar
  2. 2.
    P. Glaister, An approximate linearized Riemann solver for the Euler equations in one dimension for real gases, J. Comput. Phys. 74 (1988) 382–408.Google Scholar
  3. 3.
    S. Srinivasan, J.C. Tannehill and K.J. Weilmuenster, Simplified curve fits for the thermodynamics properties of equilibrium air, Iowa State University Engineering Institute Project 1626 (1986).Google Scholar
  4. 4.
    S.K. Godunov, A difference method for the numerical computation of continuous solutions of hydrodynamic equations, Mat. Sbornik, 47 (1959) 271–306.Google Scholar
  5. 5.
    P.K. Sweby, High resolution schemes using flux limiters for hyperbolic conservation laws, SIAM J. Numer. Anal. 21 (1984) 995–1011.Google Scholar
  6. 6.
    P. Glaister, Shock capturing on irregular grids, Numerical Analysis Report 4–86, University of Reading (1986).Google Scholar
  7. 7.
    J. Pike, Grid adaptive algorithms for the solution of the Euler equations on irregular grids, J. Comput. Phys. 71 (1987) 194–223.Google Scholar
  8. 8.
    J.F. Thompson, Z.U.A. Warsi and C.W. Mastin, Numerical Grid Generation—Foundations and Applications. North-Holland, (1985).Google Scholar

Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • P. Glaister
    • 1
  1. 1.Department of MathematicsUniversity of ReadingWhiteknightsUK

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