A DDFV Scheme for Incompressible Navier-Stokes Equations with Variable Density

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 78)

Abstract

We consider the application of “Discrete Duality Finite Volume” methods for the simulation of incompressible heterogeneous viscous flows. We pay attention to the numerical coupling between the mass conservation and the momentum balance equations, together with the divergence free constraint.

Keywords

Finite-volume methods Incompressible navier-stokes system Multifluid flows DDFV scheme 

References

  1. 1.
    Andreianov, B., Boyer, F., Hubert, F.: Discrete duality finite volume schemes for leray-lions type elliptic problems on general 2d-meshes. Numer. Methods PDE 23(1), 145–195 (2007)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Boyer, F., Krell, S., Nabet, F.: Inf-Sup Stability of the Discrete Duality Finite Volume Method for the Stokes Problem, Preprint, Inria-CNRS-Univ. Nice (2014)Google Scholar
  3. 3.
    Calgaro, C., Creusé, E., Goudon, T.: An hybrid finite volume-finite element method for variable density incompressible flows. J. Comput. Phys. 227(9), 4671–4696 (2008). http://math.univ-lille1.fr/simpaf/SITE-NS2DDV/home.html
  4. 4.
    Coudière, Y., Manzini, G.: The discrete duality finite volume method for convection-diffusion problems. SIAM J. Numer. Anal. 47(6), 4163–4192 (2010)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Droniou, J., Eymard, R.: Study of the mixed finite volume method for stokes and navier-stokes equations. Num. Meth. PDEs 25(1), 137–171 (2009)CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Domelevo, K., Omnès, P.: A finite volume method for the laplace equation on almost arbitrary two-dimensional grids. Math. Model. Numer. Anal. 39(6), 1203–1249 (2005)CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Eymard, R., Herbin, R., Latché, J.-C.: Convergence analysis of a colocated finite volume scheme for the incompressible navier-stokes equations on general 2d or 3d meshes. SIAM J. Numer. Anal. 45(1), 1–36 (2007)CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Goudon, T., Vasseur, A.: On a Model for Mixture Flows: Derivation, Dissipation and Stability Properties. Preprint. Inria-CNRS-Univ. Nice (2014)Google Scholar
  9. 9.
    Hermeline, F.: A finite volume method for the approximation of diffusion operators on distorted meshes. J. Comput. Phys. 160(2), 481–499 (2000)CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Krell, S.: Stabilized DDFV schemes for Stokes problem with variable viscosity on general 2D meshes. Num. Meth. PDEs, (2011). http://dx.doi.org/10.1002/num.20603
  11. 11.
    Krell, S.: Stabilized DDFV schemes for the incompressible Navier-Stokes equations. In: Proceedings of FVCA6 (Praha), Springer Proceedings in Math, vol. 4, pp. 605–612. (2011)Google Scholar
  12. 12.
    Krell, S., Manzini, G.: The discrete duality finite volume method for the stokes equations on 3d polyhedral meshes. SIAM J. Numer. Anal. 50(2), 808–837 (2012)CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Nagtegaal, J.C., Parks, D.M., Rice, J..R.: On numerically accurate finite element solution in the fully plastic range. Comput. Meth. Appl. Mech Eng. 4,153–177 (1974)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.INRIA, Team COFFEE and Labo. J. A. DieudonnéUniversity Nice Sophia Antipolis-CNRS UMR 7351NiceFrance

Personalised recommendations