×

zbMATH — the first resource for mathematics

An implicit integral formulation for the modeling of inviscid fluid flows in domains containing obstacles. (English) Zbl 1365.76303
Cancès, Clément (ed.) et al., Finite volumes for complex applications VIII – hyperbolic, elliptic and parabolic problems. FVCA 8, Lille, France, June 12–16, 2017. Cham: Springer (ISBN 978-3-319-57393-9/hbk; 978-3-319-57394-6/ebook; 978-3-319-58818-6/set). Springer Proceedings in Mathematics & Statistics 200, 53-61 (2017).
Summary: We focus here on an integral approach to compute compressible inviscid fluid flows in physical domains cluttered up with many small obstacles. This approach is based on a multidimensional porous integral formulation of Euler system of equations. Its discretization uses a first order semi-implicit finite volume scheme with pressure-correction algorithm preserving the positivity of both density and pressure. Numerical tests are completed by simulating a 2D channel flow containing two aligned tubes. The results are compared to reference solutions obtained with a pure fluid approach on a fine mesh.
For the entire collection see [Zbl 1371.65001].
MSC:
76S05 Flows in porous media; filtration; seepage
76M12 Finite volume methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
35Q31 Euler equations
Software:
THYC; FLICA-4
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Archambeau, F., Hérard, J.M., Laviéville, J.: Comparative study of pressure-correction and Godunov-type schemes on unsteady compressible cases. Comput. Fluids 38, 1495–1509 (2009) · Zbl 1242.76152
[2] Colas, C., Ferrand, M., Hérard, J.M., Le Coupanec, E.: Approche intégrale pour la modélisation des écoulements en milieux encombrés - Prise en compte des effets visqueux. Note interne 6125-3013-2016-17220-FR, EDF R&D (2016)
[3] Dubois, F.: Boundary conditions and the Osher scheme for the Euler equations of gas dynamics. Internal Report CMAP 170, Ecole Polytechnique, Palaiseau, France (1987)
[4] EDF R&D. http://code-saturne.org/cms/sites/default/files/docs/4.2/theory.pdf:
Code_Saturne 4.2.0 Theory Guide (2015)
[5] Ferrand, M., Hérard, J.M., Le Coupanec, E., Martin, X.: Schémas implicites dans une formulation intégrale pour la prise en compte d’obstacles immergés dans un fluide compressible. Note interne H-I83-2015-05276-FR, EDF R&D (2015)
[6] Hérard, J.M., Martin, X.: An integral approach to compute compressible fluid flows in domains containing obstacles. Int. J. Finite Vol. 12(1), 1–39 (2015)
[7] Le Coq, G., Aubry, S., Cahouet, J., Lequesne, P., Nicolas, G., Pastorini, S.: The THYC computer code. A finite volume approach for 3 dimensional two-phase flows in tube bundles. Bulletin de la Direction des études et recherches - Électricité de France, pp. 61–76 (1989)
[8] Martin, X.: Modélisation d’écoulements fluides en milieu encombré d’obstacles. Ph.D. thesis. Aix-Marseille Université (2015). https://tel.archives-ouvertes.fr/tel-01235089/
[9] Toumi, I., Bergeron, A., Gallo, D., Royer, E., Caruge, D.: FLICA-4: A three-dimensional two-phase flow computer code with advanced numerical methods for nuclear applications. Nucl. Eng. Des. 200, 139–155 (2000)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.