Details
| Original language | English |
|---|---|
| Pages (from-to) | 1049-1070 |
| Number of pages | 22 |
| Journal | Computational mechanics |
| Volume | 59 |
| Issue number | 6 |
| Publication status | Published - 21 Feb 2017 |
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.
Keywords
- Advection–reaction equations, Finite element, Numerical dissipation and dispersion, TDG–SUPG; TDG–FIC
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Ocean Engineering
- Engineering(all)
- Mechanical Engineering
- Computer Science(all)
- Computational Theory and Mathematics
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Computational mechanics, Vol. 59, No. 6, 21.02.2017, p. 1049-1070.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A spatially stabilized TDG based finite element framework for modeling biofilm growth with a multi-dimensional multi-species continuum biofilm model
AU - Feng, Dianlei
AU - Neuweiler, Insa
AU - Nackenhorst, Udo
N1 - Funding information: This work is financially supported by the doctoral program “Multifunctional Active and Reactive Interfaces and Surfaces (MARIO)” at Leibniz Universität Hannover funded by the State of Lower Saxony in Germany. The authors would like to thank to Dr. Alexander Sapotnick for many helpful discussions. They also thank to Leibniz Universität IT Services for computing power support.
PY - 2017/2/21
Y1 - 2017/2/21
N2 - 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.
AB - 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.
KW - Advection–reaction equations
KW - Finite element
KW - Numerical dissipation and dispersion
KW - TDG–SUPG; TDG–FIC
UR - http://www.scopus.com/inward/record.url?scp=85013428404&partnerID=8YFLogxK
U2 - 10.15488/1259
DO - 10.15488/1259
M3 - Article
AN - SCOPUS:85013428404
VL - 59
SP - 1049
EP - 1070
JO - Computational mechanics
JF - Computational mechanics
SN - 0178-7675
IS - 6
ER -