Details
| Original language | English |
|---|---|
| Pages (from-to) | 31-53 |
| Number of pages | 23 |
| Journal | Journal of computational physics |
| Volume | 396 |
| Early online date | 27 Jun 2019 |
| Publication status | Published - 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.
Keywords
- Advection-diffusion-reaction equation, Biofilm modeling, Burgers' equation, Finite element method, Time-space FCT
ASJC Scopus subject areas
- Mathematics(all)
- Numerical Analysis
- Mathematics(all)
- Modelling and Simulation
- Physics and Astronomy(all)
- Physics and Astronomy (miscellaneous)
- Physics and Astronomy(all)
- General Physics and Astronomy
- Computer Science(all)
- Computer Science Applications
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Journal of computational physics, Vol. 396, 01.11.2019, p. 31-53.
Research output: Contribution to journal › Article › Research › 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 -