Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 31-53 |
| Seitenumfang | 23 |
| Fachzeitschrift | Journal of computational physics |
| Jahrgang | 396 |
| Frühes Online-Datum | 27 Juni 2019 |
| Publikationsstatus | Veröffentlicht - 1 Nov. 2019 |
Abstract
We present a time-space flux-corrected transport (FCT) finite element formulation for the multi-dimensional time-dependent advection-diffusion-reaction equation. Monotonic solutions can be achieved with the presented method while large time steps (with Courant number Cr>1) are used. Numerical verification, as well as a grid convergence analysis, are carried out for 1D and 2D benchmark problems. A 1D Burgers' equation with various Reynolds numbers is solved with the time-space FCT method. In addition, a 2D transport problem with (and without) a nonlinear reaction inside of a cavity is considered. Finally, the newly developed time-space FCT formulation is applied for modeling biofilm growth problems based on a continuum mathematical model. It turns out that the time-space FCT method helps to reduce numerical dissipation and guarantees comparable numerical dispersion of the solution at the same time comparing to numerical solutions obtained by a time-space finite incremental calculus (FIC) method.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Numerische Mathematik
- Mathematik (insg.)
- Modellierung und Simulation
- Physik und Astronomie (insg.)
- Physik und Astronomie (sonstige)
- Physik und Astronomie (insg.)
- Allgemeine Physik und Astronomie
- Informatik (insg.)
- Angewandte Informatik
- Mathematik (insg.)
- Computational Mathematics
- Mathematik (insg.)
- Angewandte Mathematik
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in: Journal of computational physics, Jahrgang 396, 01.11.2019, S. 31-53.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - A time-space flux-corrected transport finite element formulation for solving multi-dimensional advection-diffusion-reaction equations
AU - Feng, Dianlei
AU - Neuweiler, Insa
AU - Nackenhorst, Udo
AU - Wick, Thomas
PY - 2019/11/1
Y1 - 2019/11/1
N2 - We present a time-space flux-corrected transport (FCT) finite element formulation for the multi-dimensional time-dependent advection-diffusion-reaction equation. Monotonic solutions can be achieved with the presented method while large time steps (with Courant number Cr>1) are used. Numerical verification, as well as a grid convergence analysis, are carried out for 1D and 2D benchmark problems. A 1D Burgers' equation with various Reynolds numbers is solved with the time-space FCT method. In addition, a 2D transport problem with (and without) a nonlinear reaction inside of a cavity is considered. Finally, the newly developed time-space FCT formulation is applied for modeling biofilm growth problems based on a continuum mathematical model. It turns out that the time-space FCT method helps to reduce numerical dissipation and guarantees comparable numerical dispersion of the solution at the same time comparing to numerical solutions obtained by a time-space finite incremental calculus (FIC) method.
AB - We present a time-space flux-corrected transport (FCT) finite element formulation for the multi-dimensional time-dependent advection-diffusion-reaction equation. Monotonic solutions can be achieved with the presented method while large time steps (with Courant number Cr>1) are used. Numerical verification, as well as a grid convergence analysis, are carried out for 1D and 2D benchmark problems. A 1D Burgers' equation with various Reynolds numbers is solved with the time-space FCT method. In addition, a 2D transport problem with (and without) a nonlinear reaction inside of a cavity is considered. Finally, the newly developed time-space FCT formulation is applied for modeling biofilm growth problems based on a continuum mathematical model. It turns out that the time-space FCT method helps to reduce numerical dissipation and guarantees comparable numerical dispersion of the solution at the same time comparing to numerical solutions obtained by a time-space finite incremental calculus (FIC) method.
KW - Advection-diffusion-reaction equation
KW - Biofilm modeling
KW - Burgers' equation
KW - Finite element method
KW - Time-space FCT
UR - http://www.scopus.com/inward/record.url?scp=85068234598&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2019.06.053
DO - 10.1016/j.jcp.2019.06.053
M3 - Article
AN - SCOPUS:85068234598
VL - 396
SP - 31
EP - 53
JO - Journal of computational physics
JF - Journal of computational physics
SN - 0021-9991
ER -