Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Computational Mechanics
Erschienen in: Computational Mechanics 6/2017

21.02.2017 | Original Paper

A spatially stabilized TDG based finite element framework for modeling biofilm growth with a multi-dimensional multi-species continuum biofilm model

Erschienen in: Computational Mechanics | Ausgabe 6/2017

Einloggen

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

search-config
loading …

Abstract

We consider a model for biofilm growth in the continuum mechanics framework, where the growth of different components of biomass is governed by a time dependent advection–reaction equation. The recently developed time-discontinuous Galerkin (TDG) method combined with two different stabilization techniques, namely the Streamline Upwind Petrov Galerkin (SUPG) method and the finite increment calculus (FIC) method, are discussed as solution strategies for a multi-dimensional multi-species biofilm growth model. The biofilm interface in the model is described by a convective movement following a potential flow coupled to the reaction inside of the biofilm. Growth limiting substrates diffuse through a boundary layer on top of the biofilm interface. A rolling ball method is applied to obtain a boundary layer of constant height. We compare different measures of the numerical dissipation and dispersion of the simulation results in particular for those with non-trivial patterns. By using these measures, a comparative study of the TDG–SUPG and TDG–FIC schemes as well as sensitivity studies on the time step size, the spatial element size and temporal accuracy are presented.
Vorheriger Artikel Cross-sectional mapping for refined beam elements with applications to shell-like structures

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
Literatur
1.
Albero AB, Ehret AE, Böl M (2014) A new approach to the simulation of microbial biofilms by a theory of fluid-like pressure-restricted finite growth. Comput Methods Appl Mech Eng 272:271–289MathSciNetCrossRefMATH
2.
Alpkvist E, Klapper I (2007) A multidimensional multispecies continuum model for heterogeneous biofilm development. Bull Math Biol 69(2):765–789CrossRefMATH
3.
Brooks AN, Hughes TJ (1982) Streamline upwind/petrov-galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier-stokes equations. Comput Methods Appl Mech Eng 32(1–3):199–259MathSciNetCrossRefMATH
4.
Chen S, Merriman B, Osher S, Smereka P (1997) A simple level set method for solving stefan problems. J Comput Phys 135(1):8–29MathSciNetCrossRefMATH
5.
Clarelli F, Di Russo C, Natalini R, Ribot M (2013) A fluid dynamics model of the growth of phototrophic biofilms. J Math Biol 66(7):1387–1408MathSciNetCrossRefMATH
6.
Codina R (1998) Comparison of some finite element methods for solving the diffusion–convection–reaction equation. Comput Methods Appl Mech Eng 156(1):185–210MathSciNetCrossRefMATH
7.
Cogan N, Keener JP (2004) The role of the biofilm matrix in structural development. Math Med Biol 21(2):147–166CrossRefMATH
8.
Costerton JW, Stewart PS, Greenberg E (1999) Bacterial biofilms: a common cause of persistent infections. Science 284(5418):1318–1322CrossRef
9.
D’Acunto B, Frunzo L, Klapper I, Mattei MR (2015) Modeling multispecies biofilms including new bacterial species invasion. Math Biosci 259:20–26MathSciNetCrossRefMATH
10.
Donea J, Huerta A (2003) Finite element methods for flow problems. Wiley, New JerseyCrossRef
11.
Duddu R, Bordas S, Chopp D, Moran B (2008) A combined extended finite element and level set method for biofilm growth. Int J Numer Meth Eng 74(5):848–870MathSciNetCrossRefMATH
12.
Duddu R, Chopp DL, Voorhees P, Moran B (2011) Diffusional evolution of precipitates in elastic media using the extended finite element and the level set methods. J Comput Phys 230(4):1249–1264MathSciNetCrossRefMATH
13.
Eberl HJ, Sudarsan R (2008) Exposure of biofilms to slow flow fields: the convective contribution to growth and disinfection. J Theor Biol 253(4):788–807MathSciNetCrossRef
14.
Eberl HJ, Picioreanu C, Heijnen J, Van Loosdrecht MC (2000) A three-dimensional numerical study on the correlation of spatial structure, hydrodynamic conditions, and mass transfer and conversion in biofilms. Chem Eng Sci 55(24):6209–6222CrossRef
15.
Eberl HJ, Parker DF, Van Loosdrecht MC (2001) A new deterministic spatio-temporal continuum model for biofilm development. Comput Math Methods Med 3(3):161–175MATH
16.
Esser DS, Leveau JHJ, Meyer KM (2015) Modeling microbial growth and dynamics. Appl Microbiol Biotechnol 99(21):8831–8846CrossRef
17.
Gebara F (1999) Activated sludge biofilm wastewater treatment system. Water Res 33(1):230–238CrossRef
18.
Gibou F, Fedkiw RP, Cheng LT, Kang M (2002) A second-order-accurate symmetric discretization of the Poisson equation on irregular domains. J Comput Phys 176(1):205–227MathSciNetCrossRefMATH
19.
20.
Gray WG, Pinder GF (1976) An analysis of the numerical solution of the transport equation. Water Resour Res 12(3):547–555CrossRef
21.
22.
Horn H, Lackner S (2014) Modeling of biofilm systems: a review. Adv Biochem Eng/Biotechnol 146:53–76CrossRef
23.
Hughes TJ, Hulbert GM (1988) Space-time finite element methods for elastodynamics: formulations and error estimates. Comput Methods Appl Mech Eng 66(3):339–363MathSciNetCrossRefMATH
24.
25.
Hundsdorfer W, Verwer JG (2003) Numerical solution of time-dependent advection–diffusion–reaction equations, vol 33. Springer, New YorkCrossRefMATH
26.
27.
28.
29.
Krause R, Mücke R, Rank E (1995) hp-version finite elements for geometrically non-linear problems. Commun Numer Methods Eng 11(11):887–897CrossRefMATH
30.
Kreft JU, Picioreanu C, Wimpenny JW, Van Loosdrecht MC (2001) Individual-based modelling of biofilms. Microbiology 147(11):2897–2912CrossRef
31.
Laspidou CS, Rittmann BE (2002) A unified theory for extracellular polymeric substances, soluble microbial products, and active and inert biomass. Water Res 36(11):2711–2720CrossRef
32.
LeVeque RJ (2002) Finite volume methods for hyperbolic problems, vol 31. Cambridge University Press, CambridgeCrossRefMATH
33.
Mabrouk N, Deffuant G, Tolker-Nielsen T, Lobry C (2010) Bacteria can form interconnected microcolonies when a self-excreted product reduces their surface motility: evidence from individual-based model simulations. Theory Biosci 129(1):1–13CrossRef
34.
de Miranda S, Mancuso M, Ubertini F (2010) Time discontinuous galerkin methods with energy decaying correction for non-linear elastodynamics. Int J Numer Meth Eng 83(3):323–346MathSciNetMATH
35.
Murray JD (2001) Mathematical biology II: spatial models and biomedical applications. Springer, New York
36.
Nackenhorst U, Ziefle M, Suwannachit A (2010) Finite element techniques for rolling rubber wheels. In: Elastomere friction. Springer, pp 123–163
37.
Oñate E, Miquel J, Zárate F (2007) Stabilized solution of the multidimensional advection–diffusion–absorption equation using linear finite elements. Comput Fluids 36(1):92–112CrossRefMATH
38.
Osher S, Fedkiw R (2006) Level set methods and dynamic implicit surfaces, vol 153. Springer, New YorkMATH
39.
40.
Picioreanu C, Van Loosdrecht MC, Heijnen JJ (2000) Effect of diffusive and convective substrate transport on biofilm structure formation: a two-dimensional modeling study. Biotechnol Bioeng 69(5):504–515CrossRef
41.
Rachowicz W, Oden J, Demkowicz L (1989) Toward a universal h–p adaptive finite element strategy part 3. Design of h–p meshes. Comput Methods Appl Mech Eng 77(1):181–212CrossRefMATH
42.
Reichert P (1998) AQUASIM 2.0: computer program for the identification and simulation of aquatic systems, PEAK, vol Basiskurs B7/98. Swiss Federal Institute for Environmental Science and Technology (EAWAG), Dübendorf
43.
Sapotnick A, Nackenhorst U (2012) A combined FIC–TDG finite element approach for the numerical solution of coupled advection-diffusion-reaction equations with application to a bioregulatory model for bone fracture healing. Int J Numer Meth Eng 92(3):301–317MathSciNetCrossRefMATH
44.
Sherratt JA, Dallon JC (2002) Theoretical models of wound healing: past successes and future challenges. Comptes Rendus Biol 325(5):557–564CrossRef
45.
Soleimani M, Wriggers P, Rath H, Stiesch M (2016) Numerical simulation and experimental validation of biofilm in a multi-physics framework using an SPH based method. Comput Mech 58(4):619–633MathSciNetCrossRefMATH
46.
Wang Q, Zhang T (2010) Review of mathematical models for biofilms. Solid State Commun 150(21–22):1009–1022CrossRef
47.
Wanner O, Gujer W (1986) A multispecies biofilm model. Biotechnol Bioeng 28(3):314–328CrossRef
48.
Wanner O, Reichert P (1996) Mathematical modeling of mixed-culture biofilms. Biotechnol Bioeng 49(2):172–184CrossRef
49.
Wimpenny JW, Colasanti R (1997) A unifying hypothesis for the structure of microbial biofilms based on cellular automaton models. FEMS Microbiol Ecol 22(1):1–16CrossRef
50.
Wise SM, Lowengrub JS, Frieboes HB, Cristini V (2008) Three-dimensional multispecies nonlinear tumor growthi: model and numerical method. J Theor Biol 253(3):524–543CrossRef
51.
Xu Z, Meakin P, Tartakovsky A, Scheibe TD (2011) Dissipative-particle-dynamics model of biofilm growth. Phys Rev E 83(6):066,702CrossRef
52.
Zhang T, Cogan N (2008a) Phase field models for biofilms. II. 2-d numerical simulations of biofilm–flow interaction. Commun Comput Phys 4(1):72–101
53.
Zhang T, Cogan NG, Wang Q (2008b) Phase field models for biofilms. I. Theory and one-dimensional simulations. SIAM J Appl Math 69(3):641–669MathSciNetCrossRefMATH
54.
Zienkiewicz OC, Taylor RL (2000) The finite element method: the basis, vol 1. Butterworth-Heinemann, OxfordMATH
Metadaten
Titel
A spatially stabilized TDG based finite element framework for modeling biofilm growth with a multi-dimensional multi-species continuum biofilm model
Publikationsdatum
21.02.2017
Erschienen in
Computational Mechanics / Ausgabe 6/2017
Print ISSN: 0178-7675
Elektronische ISSN: 1432-0924
DOI
https://doi.org/10.1007/s00466-017-1388-1

Weitere Artikel der Ausgabe 6/2017

Computational Mechanics 6/2017 Zur Ausgabe

Original Paper

Three embedded techniques for finite element heat flow problem with embedded discontinuities

Original Paper

Cross-sectional mapping for refined beam elements with applications to shell-like structures

Original Paper

Geometric constraints for shape and topology optimization in architectural design

Original Paper

Reduced order variational multiscale enrichment method for thermo-mechanical problems

Original Paper

An effective meshfree reproducing kernel method for buckling analysis of cylindrical shells with and without cutouts

Original Paper

Extended variational theory of complex rays in heterogeneous Helmholtz problem

Neuer Inhalt

    Bildnachweise