nach oben

Journal of Engineering Mathematics

Erschienen in:

01.06.2015

Asymptotic analysis of Rayleigh–Taylor flow for Newtonian miscible fluids

verfasst von: N. Schneider, S. Gauthier

Erschienen in: Journal of Engineering Mathematics | Ausgabe 1/2015

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

Asymptotic analysis is used to derive anelastic, quasi-isobaric, and Boussinesq approximations for Rayleigh–Taylor induced flow between Newtonian fluids. The anelastic approximation appears to be valid for slightly stratified equilibrium states, but the analysis does not provide bounds on the Atwood number. The quasi-isobaric model is valid for unstratified equilibrium states without bounds on the Atwood number, while the Boussinesq approximation is a restriction of the quasi-isobaric model for vanishing Atwood numbers. These three models are consistently derived from first principles within the same framework, and they greatly facilitate investigations – including some compressibility effects – of Rayleigh–Taylor flow.

Vorheriger Artikel Combined effects of fluid inertia forces and non-Newtonian rheology in circular stepped squeeze film disks

Nächster Artikel Slip flow and heat transfer over a specific wedge: an exactly solvable Falkner–Skan equation

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Nur mit Berechtigung zugänglich

Abarzhi S, Gauthier S, Niemela J (2010) Preface: turbulent mixing and beyond. Phys Scr T142:011001–014070CrossRefADS

Abarzhi S, Gauthier S, Sreenivasan K (2013) Turbulent mixing and beyond: non-equilibrium processes from atomistic to astrophysical scales II. Introduction. Philos Trans R Soc A 371(2003):7–20120436CrossRefMathSciNet

Le Creurer B, Gauthier S (2008) A return toward equilibrium in a two-dimensional Rayleigh–Taylor flows instability for compressible miscible fluids. Theor Comput Fluid Dyn 22:125–144CrossRefMATH

Chu B, Kovásznay L (1957) Non-linear interactions in a viscous heat-conducting compressible gas. J Fluid Mech 3:494–514CrossRefADS

Zeytounian R (1990) Asymptotic modeling of atmospheric flows. Springer, BerlinCrossRefMATH

Fröhlich J (1990) Résolution numérique des équations de Navier-Stokes à faible nombre de Mach par méthode spectrale. Ph.D. thesis, Université de Nice-Sophia Antipolis

Klein R, Botta N, Schneider T, Munz C, Roller S, Meister A, Hoffmann L, Sonar T (2001) Asymptotic adaptive methods for multi-scale problems in fluid mechanics. J Eng Math 39:261–343CrossRefMATHMathSciNet

Batchelor G (1953) The conditions for dynamical similarity of motions of a frictionless perfect-gas atmosphere. Q J R Meteorol Soc 79:224–235CrossRefADS

Ogura Y, Phillips N (1962) Scale analysis of deep and shallow convection in the atmosphere. J Atmos Sci 19:173–179CrossRefADS

10.

Gough D (1969) The anelastic approximation for thermal convection. J Atmos Sci 26:448–456CrossRefADS

11.

Wilhelmson R, Ogura Y (1972) The pressure perturbation and the numerical modeling of a cloud. J Atmos Sci 29(7):1295–1307CrossRefADS

12.

Lipps F, Hemler R (1982) A scale analysis of deep moist convection and some related numerical calculations. J Atmos Sci 39:2192–2210CrossRefADS

13.

Durran D (1989) Improving the anelastic approximation. J Atmos Sci 46:1453–1461CrossRefADS

14.

Emanuel K (1994) Atmospheric convection. Oxford University Press, Oxford

15.

Durran D (1999) Numerical methods for wave equations in geophysical fluid dynamics. Texts in Applied Mathematics Springer, New York

16.

Chassaing P, Antonia R, Anselmet F, Joly L, Sarkar S (2002) Variable density fluid turbulence, fluid mechanics and its applications. Kluwer Academic Publishers, DordrechtCrossRef

17.

Rehm R, Baum H (1978) The equations of motion for thermally driven buoyant flows. J Res Natl Bur Stand 83:297–308CrossRefMATH

18.

Paolucci S (1982) On the filtering of sound from the Navier–Stokes equations. SAND82-8257, Sandia National Laboratories.

19.

Majda A, Sethian J (1985) The derivation and numerical solution of the equations for zero Mach number combustion. Combust Sci Technol 42:185–205CrossRef

20.

Chenoweth D, Paolucci S (1986) Natural convection in an enclosed vertical air layer with large horizontal temperature differences. J Fluid Mech 169:173–210CrossRefADSMATH

21.

Paolucci S, Chenoweth D (1987) Departures from the Boussinesq approximation in laminar Bénard convection. Phys Fluids 30:1561–1564CrossRefADS

22.

Fröhlich J, Laure P, Peyret R (1992) Large departures from Boussinesq approximation in the Rayleigh-Bénard problem. Phys Fluids A4:1355–1372CrossRefADS

23.

Fröhlich J, Gauthier S (1993) Numerical investigations from compressible to isobaric Rayleigh–Bénard convection in two dimensions. Eur J Mech B/Fluids 2:141–159

24.

Müller B (1998) Low-Mach-number asymptotics of the Navier–Stokes equations. J Eng Math 34:10–97CrossRef

25.

Hirschfelder J, Curtiss C, Bird R (1954) Molecular theory of gases and liquids. John Wiley & Sons, New YorkMATH

26.

Cook A (2009) Enthalpy diffusion in multicomponent flows. Phys Fluids 21:16–055109CrossRef

27.

Strikwerda J (1977) Initial boundary value problems for incompletely systems. Commun Pure Appl Math 30:797–822CrossRefMATHMathSciNet

28.

Bazarov I (1964) Thermodynamics. Macmillan, New York

29.

Guo W, Labrosse G, Narayanan R (2012) The application of the Chebyshev-spectral method in transport phenomena. Lecture Notes in Applied and Computational Mechanics. Springer, New York

30.

Hammouch Z, Labrosse G, Gauthier S (2013) Anelastic Stokes eigenmodes in infinite channel. J Sci Comput 55:65–91CrossRefMATHMathSciNet

31.

Tryggvason G (1983) In: Mellor F (ed) Geophysical fluid dynamics, vol WHOI-83-41. pp 207–228

32.

Canuto C, Hussaini M, Quarteroni A, Zang T (1988) Spectral methods in fluid dynamics. Springer, BerlinCrossRefMATH

33.

Peyret R (2002) Spectral methods for incompressible viscous flow. Springer, New YorkCrossRefMATH

34.

Labrosse G (2011) Méthodes spectrales. Ellipses, Paris

35.

Fröhlich J, Peyret R (1990) Calculations of non-Boussinesq convection by a pseudo-spectral method. Comput Methods Appl Mech Eng 80:425–433CrossRefADSMATH

36.

Fröhlich J, Peyret R (1992) Direct spectral methods for the low Mach number equations. Int J Numer Heat Fluid Flow 2:195–213CrossRef

37.

Gauthier S, Le Creurer B, Abéguilé F, Boudesocque-Dubois C, Clarisse JM (2005) A self-adaptative domain decomposition method with Chebyshev method. Int J Pure Appl Math 24(4):553–577MATHMathSciNet

38.

Barranco J, Marcus P (2006) A 3D spectral anelastic hydrodynamic code for shearing, stratified flows. J Comput Phys 219:21–46CrossRefADSMATHMathSciNet

39.

Schneider N, Hammouch Z, Labrosse G, Gauthier S (2014) A spectral anelastic Navier–Stokes solver for a stratified two-miscible-layer system in infinite horizontal channel (in preparation)

Titel: Asymptotic analysis of Rayleigh–Taylor flow for Newtonian miscible fluids
verfasst von: N. Schneider
S. Gauthier
Publikationsdatum: 01.06.2015
Verlag: Springer Netherlands
Erschienen in: Journal of Engineering Mathematics / Ausgabe 1/2015
Print ISSN: 0022-0833
Elektronische ISSN: 1573-2703
DOI: https://doi.org/10.1007/s10665-014-9765-7

Premium Partner

Marktübersichten

Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.

Zur Marktübersicht

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Weitere Artikel der Ausgabe 1/2015

Analytical solution and mechanisms of fluid production from hydraulically fractured wells with finite fracture conductivity

A study of the effects of electric field on two-dimensional inviscid nonlinear free surface flows generated by moving disturbances

On the stability of initial conditions for the parabolic Gelfand problem

Slip flow and heat transfer over a specific wedge: an exactly solvable Falkner–Skan equation

Combined effects of fluid inertia forces and non-Newtonian rheology in circular stepped squeeze film disks

Complex material flow problems: a multi-scale model hierarchy and particle methods

Premium Partner

Marktübersichten