Skip to main content
SpringerLink
Log in

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

  • Published:
Journal of Engineering Mathematics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. P.L. Roe, Approximate Riemann solvers, parameters vectors and difference schemes, J. Comput. Phys. 49 (1983) 357–372.

    Google Scholar 

  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. 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).

  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. P.K. Sweby, High resolution schemes using flux limiters for hyperbolic conservation laws, SIAM J. Numer. Anal. 21 (1984) 995–1011.

    Google Scholar 

  6. P. Glaister, Shock capturing on irregular grids, Numerical Analysis Report 4–86, University of Reading (1986).

  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. J.F. Thompson, Z.U.A. Warsi and C.W. Mastin, Numerical Grid Generation—Foundations and Applications. North-Holland, (1985).

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Reading, P.O. Box 220, RG6 2AX, Whiteknights, Reading, UK

    P. Glaister

Authors
  1. P. Glaister
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work forms part of the research programme for the Institute of Computational Fluid Dynamics at the Universities of Oxford and Reading and was funded by AWRE, Aldermaston under Contract No. NSN/13B/2A88719.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Glaister, P. Flux difference splitting for the Euler equations in generalised coordinates using a local parameterisation of the equation of state. J Eng Math 23, 17–28 (1989). https://doi.org/10.1007/BF00058431

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00058431

Keywords

Search

Navigation