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.
The paper is in final form and no similar paper has been or is being submitted elsewhere.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
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)
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)
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
Coudière, Y., Manzini, G.: The discrete duality finite volume method for convection-diffusion problems. SIAM J. Numer. Anal. 47(6), 4163–4192 (2010)
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)
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)
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)
Goudon, T., Vasseur, A.: On a Model for Mixture Flows: Derivation, Dissipation and Stability Properties. Preprint. Inria-CNRS-Univ. Nice (2014)
Hermeline, F.: A finite volume method for the approximation of diffusion operators on distorted meshes. J. Comput. Phys. 160(2), 481–499 (2000)
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
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)
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)
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)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Goudon, T., Krell, S. (2014). A DDFV Scheme for Incompressible Navier-Stokes Equations with Variable Density. In: Fuhrmann, J., Ohlberger, M., Rohde, C. (eds) Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems. Springer Proceedings in Mathematics & Statistics, vol 78. Springer, Cham. https://doi.org/10.1007/978-3-319-05591-6_62
Download citation
DOI: https://doi.org/10.1007/978-3-319-05591-6_62
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-05590-9
Online ISBN: 978-3-319-05591-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)