×

zbMATH — the first resource for mathematics

Fictiuous domain approach for numerical modelling of Navier-Stokes equations. (English) Zbl 1032.76041
A fictitiuous domain model for the numerical solution of various incompressible viscous flows is investigated. Boundaries are taken into account by a penalty technique. The scheme is an implicit upwind finite volume method on staggered Cartesian meshes. In order to increase the precision, multigrid local grid refinement is implemented together with multi-level zoom flux interface correction. Test cases are discussed.

MSC:
76M12 Finite volume methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Contribution ? l’?tude des transferts thermiques dans des syst?mes complexes; application aux composants ?lectroniques, Th?se de Doctorat de l’Universit? Bordeaux I. Sp?cialit? M?canique, Avril, 1989.
[2] Logiciel d’Ing?ni?rie Scientifique THANES, Manuel Technique, Commercialis? sous Licence no. L89043 CNRS/ENSAM/Universit? Bordeaux I, Soci?t? G5G, PA Ch?teau Rouquey?BP 168-33708 M?rignac, 1989.
[3] New graphical and computational architecture concept for numerical simulation on supercomputers. In Proceedings 2nd World Congress on Computational Mechanics, vol. 1, Stuttgart, 1990; 973-976.
[4] Angot, Hemisphere 5 pp 219– (1990)
[5] Le Projet AQUILON, D?veloppement d’un environnement informatique et graphique adapt? ? l’exp?rimentation num?rique interactive, CERFACS Technical Report, TR/VI/90/41, October, 1990.
[6] Thermal Modelling of IBM Power Single Chip Modules, IBM Technical Report, TR-47140, January, 1991.
[7] Angot, CR Acad?mie Science de Paris 315 pp 739– (1992)
[8] Angot, CR Acad?mie Science de Paris 319 pp 993– (1994)
[9] Parallel and distributed multi-domain methods for numerical fluid dynamics. In High Performance Computing in Europe on IBM Platforms, Sup’Eur 96 Conference Proceedings, (eds). ACC CYFRONET: Krak?w, 1996; 111-120.
[10] Angot, East-West Journal of Numerical Mathematics (1996)
[11] Angot, Mathematical Methods in the Applied Sciences 22 pp 1395– (1999) · Zbl 0980.65129
[12] Angot, N?merische Mathematik 81 pp 497– (1999)
[13] Finite volume methods for non-smooth solution of diffusion models; application to imperfect contact problems. In Recent Advances in Numerical Methods and Applications, Proceedings 4th International Conference of NMA 1998, (eds). World Scientific Publishing: Sofia (Bulgaria), 1999; 621-629. · Zbl 0980.65129
[14] Mathematical and numerical modelling for a fictitious domain method with penalized immersed boundary conditions. Preprint HDR Thesis, Universit? M?diterran?e Aix-Marseille, 1998.
[15] Armaly, Journal of Fluid Mechanics 127 pp 473– (1983)
[16] Arquis, CR Acad? Science de Paris 299 pp 1– (1984)
[17] Interacting convection between fluid and open porous layers, ASME WAM, Boston, Paper 87 WA/HT-24, 1987.
[18] B?rgers, SIAM Journal of Numerical Analysis 27 pp 963– (1990)
[19] B?rgers, Numeric Mathematics 57 pp 435– (1990)
[20] Simulation num?rique du d?collement instationnaire externe par une formulation vitesse-pression application ? l’?coulement autour d’un cylindre. Th?se Doctorat de I’Institut National Polytechnique de Toulouse. Sp?cialit? M?canique, 1981.
[21] Braza, Journal of Fluid Mechanics 165 pp 79– (1986)
[22] Brinkman, Applied Scientific Research A1 pp 27– (1947)
[23] Brinkman, Applied Scientific Research A1 pp 81– (1947)
[24] Briscolini, Journal of Computer Physics 84 pp 57– (1989)
[25] Bruneau, International Journal of Numerical Methods in Fluids 19 pp 693– (1994)
[26] Buzbee, SIAM Journal of Numerical Analysis 8 pp 722– (1971)
[27] Caltagirone, CR Acad?mie Science de Paris 318 pp 571– (1994)
[28] Caltagirone, CR Academie Science de Paris 320 pp 295– (1995)
[29] Cihlar, Numerical Linear Algebra with Applications 6 pp 17– (1999)
[30] Coutanceau, Journal of Fluid Mechanics 79 pp 231– (1977)
[31] Dennis, Journal of Fluid Mechanics 42 pp 471– (1970)
[32] Du?ek, Journal of Fluid Mechanics 264 pp 59– (1994)
[33] M?thodes de Lagrangien Augment?; Applications ? la R?solution Num?rique de Probl?mes aux Limites. In M?thodes Mathematique de l’Informatique, vol. 9, Dunod-Bordas: Paris, 1982.
[34] Numerical methods for non-linear variational problems. In Springer Series in Computational Physics. Springer-Verlag: New York, 1984.
[35] Glowinski, Computing Methods in Applied Mechanical Engineering 112 pp 133– (1994)
[36] Glowinski, International Journal of Numerical Methods in Fluids 20 pp 695– (1995)
[37] Goldstein, Journal of Computer Physics 105 pp 354– (1993)
[38] Gresho, Annual Review of Fluid Mechanics 23 pp 413– (1991)
[39] Grove, Journal of Fluid Mechanics 19 pp 60– (1965)
[40] Hamielec, Physical Fluids 12 pp 11– (1969)
[41] D?collement provoqu? d’un ?coulement turbulent incompressible. Th?se de Doctorat d’Etat. I.N.P. Toulouse, 1976.
[42] Hammache, Journal of Fluid Mechanics 232 pp 567– (1991)
[43] The potential calculation and some applications. In Methods in Computational Physics, vol. 9, (eds). Academic Press: London, 1969; 136-211.
[44] Kaiktsis, Journal of Fluid Mechanics 231 pp 501– (1991)
[45] Karniadakis, International Journal of Heat Mass Transfer 31 pp 107– (1988)
[46] Karniadakis, Journal of Fluid Mechanics 199 pp 441– (1989)
[47] Karniadakis, Journal of Fluid Mechanics 238 pp 1– (1992)
[48] A comparison of locally adaptative multigrid methods: L.D.C., F.A.C. and F.L.C.. In Sixth Copper Mountain Conference on Multigrid Methods, vol. 1, (eds). NASA Conference Publication CP-3224: Hampton, VA, 1993; 275-292.
[49] M?thodes adaptatives de raffinement local multigrille; applications aux quations de Navier-Stokes et de l’?nergie. Th?se de Doctorat de l’Universit? Bordeaux I, Sp?cialit? Math?matiques Appliqu?es, Mars, 1994.
[50] Khadra, Mathematical Modelling and Numerical Analysis 30 pp 39– (1996)
[51] Computation of the Navier-Stokes and thermal equations by multigfid local mesh refinement methods. In Advanced Concepts and Techniques in Thermal Modelling, (eds). Elsevier: New York/Amsterdam, 1996; 83-89.
[52] Laugier, International Journal Numerical Methods in Fluids 23 pp 1163– (1996)
[53] Leonard, Computing Methods in Applied Mechanical Engineering 19 pp 59– (1979)
[54] Methods of numerical mathematics. In Application of Maths, vol. 2, Springer-Verlag: New York, 1982.
[55] Marchuk, Soviet Journal of Numerical Analysis in Mathematic Modelling 1 pp 3– (1986)
[56] Simulation des ?coulements turbulents et des transferts thermiques en vue de l’optimisation du refroidissement des pales de turbine. Th?se de Doctorat de l’Universit? Bordeaux I, Sp?cialit? M?canique, Juillet, 1995.
[57] Simulation num?rique directe de la turbulence par une m?thode de raffinement local multigrille. 31?me colloque d’A?rodynamique Appliqu?e, AAAF, 1995.
[58] Numerical Heat Transfer and Fluid Flow. Hemisphere: Washington DC, 1980.
[59] Peskin, Journal of Computer Physics 25 pp 220– (1977)
[60] Computational methods for fluid flow. In Springer Series in Computational Physics. Springer-Verlag: New York, 1983. · Zbl 0514.76001
[61] Mod?lisation des ?coulements tridimensionnels turbulents dans une pale de turbine. Th?se de Doctorat de l’Universit? Bordeaux I, Sp?cialit? Math?matiques Appliqu?es, Decembre, 1992.
[62] Saiki, Journal of Computer Physics 123 pp 450– (1996)
[63] Son, Journal of Fluid Mechanics 35 pp 369– (1969)
[64] Phuoc Loc, Journal M?canique 14 pp 109– (1975)
[65] Tritton, Journal of Fluid Mechanics 45 pp 203– (1971)
[66] Tuann, Computers and Fluids 6 pp 219– (1978)
[67] Van Der Vorst, SIAM Journal of Scientific Statistics in Computing 13 pp 631– (1992)
[68] Williamson, Journal of Fluid Mechanics 206 pp 579– (1989)
[69] Chang, International Communications in Heat and Mass Transfer 16 pp 427– (1989)
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.