Abstract
We consider DDFV discretization of the Navier-Stokes equations where the convection fluxes are computed by means of B-schemes, generalizing the classical centered and upwind discretizations. This study is motivated by the analysis of domain decomposition approaches. We investigate on numerical grounds the convergence of the method.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Boyer, F., Krell, S., Nabet, F.: Inf-sup stability of the discrete duality finite volume method for the 2D Stokes problem. Math. Comput. 84, 2705–2742 (2015)
Chainais-Hillairet, C., Droniou, J.: Finite volume schemes for non-coercive elliptic problems with Neumann boundary conditions. IMA J. Numer. Anal. 31, 61–85 (2011)
Coudière, Y., Vila, J.-P., Villedieu, P.: Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem. ESAIM: Math. Mod. Numer. Anal. 33(3), 493–516 (1999)
Delcourte, S., Omnes, P.: A discrete duality finite volume discretization of the vorticity-velocity-pressure formulation of the 2D Stokes problem on almost arbitrary two-dimensional grids. Numer. Methods PDEs 1–30 (2015)
Domelevo, K., Omnes, P.: A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids. ESAIM: Math. Mod. Numer. Anal. 39(6), 1203–1249 (2005)
Goudon, T., Krell, S., Lissoni, G.: DDFV method for Navier-Stokes problem with outflow boundary conditions. Numer. Math. 142(1), 55–102 (2019)
Goudon, T., Krell, S., Lissoni, G.: Non-overlapping Schwarz algorithms for the incompressible Navier-Stokes equations with DDFV discretizations. Tech. report, Univ. Côte d’Azur, Inria, CNRS, LJAD, 2019. https://hal.archives-ouvertes.fr/hal-02448007
Halpern, L., Hubert, F.: A finite volume Ventcell-Schwarz algorithm for advection-diffusion equations. SIAM J. Numer. Anal. 52(3), 1269–1291 (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. Numer. Methods PDEs 27(6), 1666–1706 (2011)
Krell, S.: Stabilized DDFV schemes for the incompressible Navier-Stokes equations. In: Finite Volumes for Complex Applications VI. Problems & Perspectives, pp. 605–612 (2011)
Lions, P.L.: On the Schwarz alternating method. III. A variant for nonoverlapping subdomains. In: Third International Symposium on Domain Decomposition Methods for Partial Differential Equations, SIAM, Philadelphia, PA, 1990, pp. 202–223
Schwarz, H.A.: Über einen grenzübergang durch alternierendes verfahren. Vierteljahrsschrift der Naturforschenden Gesellschaft in Zurich 15, 272–286 (1870)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Goudon, T., Krell, S., Lissoni, G. (2020). Convergence Study of a DDFV Scheme for the Navier-Stokes Equations Arising in the Domain Decomposition Setting. In: Klöfkorn, R., Keilegavlen, E., Radu, F.A., Fuhrmann, J. (eds) Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples. FVCA 2020. Springer Proceedings in Mathematics & Statistics, vol 323. Springer, Cham. https://doi.org/10.1007/978-3-030-43651-3_30
Download citation
DOI: https://doi.org/10.1007/978-3-030-43651-3_30
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-43650-6
Online ISBN: 978-3-030-43651-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)