Journal
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS
Volume 57, Issue 3, Pages 1691-1729Publisher
EDP SCIENCES S A
DOI: 10.1051/m2an/2023031
Keywords
TEHD Boussinesq; finite element method; error estimation
Categories
Ask authors/readers for more resources
This paper proposes a full discretization scheme for the instationary thermal-electro-hydrodynamic (TEHD) Boussinesq equations. The scheme combines an H-1-conformal finite element method for spatial discretization with a backward differentiation formula (BDF) for time stepping. A priori convergence rates are derived and special care is taken of modeling the DEP force. Numerical experiments are conducted to verify the obtained error estimates.
In this paper, we propose a full discretization scheme for the instationary thermal-electro-hydrodynamic (TEHD) Boussinesq equations. These equations model the dynamics of a non-isothermal, dielectric fluid under the influence of a dielectrophoretic (DEP) force. Our scheme combines an H-1-conformal finite element method for spatial discretization with a backward differentiation formula (BDF) for time stepping. The resulting scheme allows for a decoupled solution of the individual parts of this multi-physics system. Moreover, we derive a priori convergence rates that are of first and second order in time, depending on how the individual ingredients of the BDF scheme are chosen and of optimal order in space. In doing so, special care is taken of modeling the DEP force, since its original form is a cubic term. The obtained error estimates are verified by numerical experiments.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available