Comparison of Upwind and Centered Schemes for Low Mach Number Flows

  • Thu–Huyen DAOEmail author
  • Michael Ndjinga
  • Frédéric Magoules
Conference paper
Part of the Springer Proceedings in Mathematics book series (PROM, volume 4)


In this paper, fully implicit schemes are used for the numerical simulation of compressible flows at low Mach number. The compressible Navier–Stokes equations are discretized classically using the finite volume framework and a Roe type scheme for the convection flux. Though explicit Godunov type schemes are inaccurate for low Mach number flows on Cartesian meshes, we claim that their implicit counterpart can be more precise for that type of flow. Numerical evidence from the lid driven cavity benchmark shows that the centered implicit scheme can capture low Mach vortices, unlike the upwind scheme. We also propose a Scaling strategy based on the convection spectrum to reduce the computational cost and accelerate the convergence of both linear system and Newton scheme iterations.


Low Mach number centered scheme upwind scheme compressible flows scaling preconditioner 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    E. Godlewski, P.A. Raviart, Numerical Approximation of Hyperbolic Systems of Conservation Laws Springer Verlag, 1996.Google Scholar
  2. 2.
    P.L Roe, Approximate Riemann solvers, parameter vectors and difference schemes J. Comput. Phys., 43 (1981), 537-372.Google Scholar
  3. 3.
    Michele Benzi, Preconditioning Techniques for Large Linear Systems: A Survey J. Comput. Phys., 182 (2002), 418-477.Google Scholar
  4. 4.
    U. Ghia, K.N. Ghia, C.T. Shin, High-Re Solutions for Incompressible Flow Using the Navier-Stokes Equations and a Multigrid Method J. Comput. Phys., 48 (1982), p 387-411.Google Scholar
  5. 5.
    S. Dellacherie, Analysis of Godunov type schemes applied to the compressible Euler system at low Mach number J. Comput. Phys., 229(2010), 701-727.Google Scholar
  6. 6.
    I. Toumi, A. Bergeron, D. Gallo, and D. Caruge, FLICA-4: a three-dimensional two-phase flow computer code with advanced numerical methods for nuclear applications Nucl. Eng. Design, 200 (2000), p 139-155.Google Scholar
  7. 7.
    P. Fillion, A. Chanoine, S. Dellacherie, A. Kumbaro, FLICA-OVAP: a New Platform for Core Thermal-hydraulic Studies NURETH-13 Japon, Sep 27-Oct 2, (2009).Google Scholar
  8. 8.
    H. Guillard, C. Viozat, On the behavior of upwind schemes in the low Mach number limit Comput. Fluids 28 (1999).Google Scholar
  9. 9.
    J.-A. Désidéri, P. W. Hemker, Convergence Analysis of the Defect-Correction Iteration for Hyperbolic Problems SIAM J. Sci. Comput., Vol. 16 (1995), No.1, pp. 88-118.Google Scholar
  10. 10.
    S. Schochet, Fast Singular Limits of Hyperbolic PDEs Journal of Differential Equations 114 (1994).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Thu–Huyen DAO
    • 1
    • 2
    Email author
  • Michael Ndjinga
    • 1
  • Frédéric Magoules
    • 2
  1. 1.CEA–Saclay, DEN, DM2S, SFME, LGLSGif–sur–YvetteFrance
  2. 2.MAS, Ecole Centrale ParisChâtenay–MalabryFrance

Personalised recommendations