Finite element approximation of dielectrophoretic force driven flow problems

Abstract:
          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.

SEEK ID: https://publications.h-its.org/publications/1806

DOI: 10.1051/m2an/2023031

Research Groups: Data Mining and Uncertainty Quantification

Publication type: Journal

Journal: ESAIM: Mathematical Modelling and Numerical Analysis

Citation: ESAIM: M2AN 57(3):1691-1729

Date Published: 1st May 2023

Registered Mode: by DOI

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Citation
Gerstner, P., & Heuveline, V. (2023). Finite element approximation of dielectrophoretic force driven flow problems. In ESAIM: Mathematical Modelling and Numerical Analysis (Vol. 57, Issue 3, pp. 1691–1729). EDP Sciences. https://doi.org/10.1051/m2an/2023031
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Created: 16th Feb 2024 at 13:17

Last updated: 5th Mar 2024 at 21:25

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