nach oben

Acta Mechanica

Erschienen in:

24.06.2020 | Original Paper

A Mixed Eulerian–Lagrangian scheme for scalar transport

verfasst von: Benoît Trouette, Georges Halim Atallah, Stéphane Vincent

Erschienen in: Acta Mechanica | Ausgabe 9/2020

Einloggen, um Zugang zu erhalten

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

search-config

KI-gestützte Suche

Aus

Abstract

The tracking of pollutants in gas and liquid is a major problem to address in atmospheric environment, air quality characterization, and industrial material processes. A Lagrangian scheme devoted to the approximation of the advection term in an advection–diffusion equation is proposed to deal with small diffusivity values or large Péclet numbers. The Lagrangian scheme is used in practice as an Eulerian method discretized on Lagrangian marker points. Advection and diffusion of a circular concentration spot in a vortex flow are considered for validation purpose. The resulting mixed Eulerian–Lagrangian scheme reduces the numerical diffusion to almost computer error and provides better results than other Eulerian classical schemes of the literature. The scheme is finally illustrated in a natural convection situation.

Vorheriger Artikel Mechanics of kerf patterns for creating freeform structures

Nächster Artikel Explicit solution of one boundary value problem of thermoelasticity for a circle with diffusion, microtemperatures, and microconcentrations

Nur mit Berechtigung zugänglich

Amestoy, P.R., Duff, I.S., Koster, J., L’Excellent, J.Y.: A fully asynchronous multifrontal solver using distributed dynamic scheduling. SIAM J. Matrix Anal. Appl. 23(1), 15–41 (2001)MathSciNetMATHCrossRef

Campos, L., Gardin, P., Vincent, S., Caltagirone, J.: Physical modeling of turbulent multiphase flow in a continuous casting steel mold. Comput. Methods Multiph. Flow VIII 89, 439–450 (2015)CrossRef

Chertock, A., Kurganov, A., Petrova, G.: Fast explicit operator splitting method for convection-diffusion equations. Int. J. Numer. Methods Fluids 59(3), 309–332 (2006). https://doi.org/10.1002/fld.1355MathSciNetMATHCrossRef

Cottet, G.H.: Multi-physics and particle methods. Comput. Fluid Solid Mech. 1, 1296–1298 (2003)

Couderc, F.: Development of a numerical code for the simulation of non-miscible fluid flow. Application to the air-assisted disintegration of a liquid jet. Theses, Ecole nationale superieure de l’aeronautique et de l’espace (2007). https://tel.archives-ouvertes.fr/tel-00143709

De Vahl Davis, G., Jones, I.P.: Natural convection in a square cavity: a comparison exercise. Int. J. Numer. Methods Fluids 3(3), 227–248 (1983). https://doi.org/10.1002/fld.1650030304MATHCrossRef

Delage, S., Vincent, S., Caltagirone, J.P., Heliot, J.P.: A hybrid linking approach for solving the conservation equations with an adaptive mesh refinement method. J. Computat. Appl. Math. 191(2), 280–296 (2006)MathSciNetMATHCrossRef

Deng, L., Zhang, Y., Wen, Y., Shan, B., Zhou, H.: A fractional-step thermal lattice Boltzmann model for high Peclet number flow. Comput. Math. Appl. 70(5), 1152–1161 (2015). https://doi.org/10.1016/j.camwa.2015.07.006MathSciNetCrossRef

Devkota, B.H., Imberger, J.: Lagrangian modeling of advection–diffusion transport in open channel flow. Water Resour. Res. 45, 12 (2009)CrossRef

10.

Dugois, K., Vincent, S., Lasseux, D., Arquis, E., Descamps, C.: A macroscopic model for the impregnation process of composite material by a concentrated suspension. In: European Congress and Exhibition on Advanced Materials and Processes, Warsaw, Poland, September 20–24 (2015)

11.

Enright, D., Losasso, F., Fedkiw, R.: A fast and accurate semi-Lagrangian particle level set method. Front. Multi-Phase Flow Anal. Fluid-Struct. Comput. Struct. 83(6), 479–490 (2005)

12.

Geiser, J., Elbiomy, M.: Splitting method of convection–diffusion methods with disentanglement methods. Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik (2011). https://doi.org/10.18452/2819

13.

Grassia, P., Ubal, S.: Streamline-averaged mass transfer in a circulating drop. Chem. Eng. Sci. 190, 190–219 (2018). https://doi.org/10.1016/j.ces.2018.02.042CrossRef

14.

Guichard, R., Belut, E.: Simulation of airborne nanoparticles transport, deposition and aggregation: experimental validation of a CFD-QMOM approach. J. Aerosol Sci. 104, 16–31 (2017)CrossRef

15.

Gustafsson, I.: On First and Second Order Symmetric Factorisation Methods for the Solution of Elliptic Difference Equations. Chalmers University of Technology, Chalmers (1978)

16.

Halim Atallah, G., Trouette, B., Belut, E., Vincent, S., Lechène, S.: Les simulation of pollutant transport in ventilation-based mitigation devices. Turbulence and Interactions 2018 (TI2018), 25–29 June, Martinique, France (2018)

17.

Harlow, F., Welch, J.: Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids 8, 2182–2189 (1965)MathSciNetMATHCrossRef

18.

Hermes, V., Klioutchnikov, I., Olivier, H.: Linear stability of weno schemes coupled with explicit runge-kutta schemes. Int. J. Numer. Methods Fluids 69(6), 1065–1095 (2012)MathSciNetMATHCrossRef

19.

Hirsch, C.: Numerical Computation of Internal and External Flows: The Fundamentals of Computational Fluid Dynamics. Elsevier, London (2007)

20.

Hoover, W.: Smooth Particle Applied Mechanics. World Scientific, Singapore (2006)MATHCrossRef

21.

Jiang, G.S., Shu, C.W.: Efficient implementation of weighted eno schemes. J. Comput. Phys. 126(1), 202–228 (1996). https://doi.org/10.1006/jcph.1996.0130MathSciNetMATHCrossRef

22.

Khadra, K., Angot, P., Parneix, S., Caltagirone, J.P.: Fictitious domain approach for numerical modelling of navier-stokes equations. Int. J. Numer. Methods Fluids 34(8), 651–684 (2000)MATHCrossRef

23.

Khalili, A., Basu, A., Pietrzyk, U., Jørgensen, B.B.: Advective transport through permeable sediments: a new numerical and experimental approach. Acta Mech 132(1–4), 221–227 (1999)MATHCrossRef

24.

Koumoutsakos, P.: Multiscale flow simulations using particles. Annu. Rev. Fluid Mech. 37, 457–487 (2005)MathSciNetMATHCrossRef

25.

Le Quéré, P.: Accurate solutions to the square thermally driven cavity at high Rayleigh number. Comput. Fluids 20(1), 29–41 (1991). https://doi.org/10.1016/0045-7930(91)90025-DMATHCrossRef

26.

LeVeque, R.J.: High-resolution conservative algorithms for advection in incompressible flow. SIAM J. Numer. Anal. 33(2), 627–665 (1996)MathSciNetMATHCrossRef

27.

Liu, C.H., Barth, M.C., Leung, D.Y.: Large-eddy simulation of flow and pollutant transport in street canyons of different building-height-to-street-width ratios. J. Appl. Meteorol. 43(10), 1410–1424 (2004)CrossRef

28.

Mackowski, D.W.: Conduction heat transfer: Notes for mech 7210. Mechanical Engineering Department, Auburn University (2011)

29.

McDermott, R., Pope, S.B.: The parabolic edge reconstruction method (perm) for Lagrangian particle advection. J. Computat. Phys. 227(11), 5447–5491 (2008)MathSciNetMATHCrossRef

30.

Monaghan, J.J.: An introduction to sph. Comput. Phys. Commun. 48, 89–96 (1988)MATHCrossRef

31.

Nguyen, K., Dabdub, D.: Two-level time-marching scheme using splines for solving the advection equation. Atmos. Environ. 35(9), 1627–1637 (2001)CrossRef

32.

Poulikakos, D.: Conduction Heat Transfer (1993)

33.

Rapaport, D.C.: The Art of Molecular Dynamics Simulation. Cambridge University Press, Cambridge (2004)MATHCrossRef

34.

Rosenheinrich, W.: Tables of some indefinite integrals of Bessel functions. University of Applied Sciences, Germany (2012)

35.

Sarra, S.A.: The method of characteristics with applications to conservation laws. J. Online Math. Appl. 3, 1–16 (2003)

36.

Shadloo, M., Oger, G., Touzé, D.L.: Smoothed particle hydrodynamics method for fluid flows, towards industrial applications: motivations, current state, and challenges. Comput. Fluids 136, 11–34 (2016). https://doi.org/10.1016/j.compfluid.2016.05.029MathSciNetMATHCrossRef

37.

Shu, C.W., Osher, S.: Efficient implementation of essentially non-oscillatory shock-capturing schemes. J. Comput. Phys. 77(2), 439–471 (1988). https://doi.org/10.1016/0021-9991(88)90177-5MathSciNetMATHCrossRef

38.

Sorek, S.: Eulerian-Lagrangian method for solving transport in aquifers. Adv. Water Resour. 11(2), 67–73 (1988)CrossRef

39.

Spiegelman, M., Katz, R.F.: A semi-Lagrangian Crank-Nicolson algorithm for the numerical solution of advection-diffusion problems. Geochem. Geophys. Geosyst. 7, 4 (2006)CrossRef

40.

Sun, Z., Xiao, F.: A semi-Lagrangian multi-moment finite volume method with fourth-order weno projection. Int. J. Numer. Methods Fluids 83(4), 351–375 (2017)MathSciNetCrossRef

41.

van der Vorst, H.A.: Bi-cgstab: a fast and smoothly converging variant of bi-cg for the solution of nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 13, 631–644 (1992)MathSciNetMATHCrossRef

42.

Vincent, S., Caltagirone, J.P.: Efficient solving method for unsteady incompressible interfacial flow problems. Int. J. Numer. Methods Fluids 30(6), 795–811 (1999)MATHCrossRef

43.

Vincent, S., Balmigère, G., Caltagirone, J.P., Meillot, E.: Eulerian-Lagrangian multiscale methods for solving scalar equations-application to incompressible two-phase flows. J. Comput. Phys. 229(1), 73–106 (2010). https://doi.org/10.1016/j.jcp.2009.09.007MathSciNetMATHCrossRef

44.

Wacławczyk, M., Pozorski, J., Minier, J.P.: New molecular transport model for fdf/les of turbulence with passive scalar. Flow Turbul. Combust. 81(1–2), 235 (2008)MATHCrossRef

45.

Zahran, Y.H.: An efficient tvd-weno method for conservation laws. Numer. Methods Partial Differ. Equ. Int. J. 25(6), 1443–1467 (2009)MathSciNetMATHCrossRef

46.

Zimmermann, S., Koumoutsakos, P., Kinzelbach, W.: Simulation of pollutant transport using a particle method. J. Comput. Phys. 173(1), 322–347 (2001)MATHCrossRef

Titel: A Mixed Eulerian–Lagrangian scheme for scalar transport
verfasst von: Benoît Trouette
Georges Halim Atallah
Stéphane Vincent
Publikationsdatum: 24.06.2020
Verlag: Springer Vienna
Erschienen in: Acta Mechanica / Ausgabe 9/2020
Print ISSN: 0001-5970
Elektronische ISSN: 1619-6937
DOI: https://doi.org/10.1007/s00707-020-02727-2

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.

Weitere Artikel der Ausgabe 9/2020

Three-dimensional flow structure and mixing of the side thermal buoyant jet discharge in cross-flow

Stability of nanobeams under nonconservative surface loading

In-plane transient analysis of two dissimilar nonhomogeneous half-planes containing several interface cracks

Issues related to the second spectrum, Ostrogradsky’s energy and the stabilization of Timoshenko–Ehrenfest-type systems

The effect of bend angle on pressure drop and flow behavior in a corrugated duct

Set theoretical variants of the teaching–learning-based optimization algorithm for optimal design of truss structures with multiple frequency constraints

Premium Partner

Marktübersichten