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Author: Philipp Gerstner13
Using CutFEM for solving the linearized Poisson-Boltzmann equation: Introductory application in HiFlow3

Abstract (Expand)

The Poisson-Boltzmann equation(PBE) is a fundamental equation for accurate description of electrostatics in ionic solutions or plasma. Hence, it finds application in a wide variety of fields including … plasma physics, computational biology, colloidal and interface science and chemistry. In this preprint, we describe a first approach for solving it in a linearized setup using the CutFEM method in the software framework HiFlow3. The considered methods are easy to use, but not oriented towards extracting optimal computing time. Forthis purpose,the weak form of the linear PBE is first derived. Then, the CutFEM based numerical method is proposed. Finally, the most important code sections in HiFlow 3 are explained in more details. The electrostatic potential for ubiquitin and the adenovirus virion molecules are calculated and presented in a numerical example at the end of the paper.

Authors: Jonas Roller, Valentin Schmid, Philipp Gerstner, Jakob Nießner, Vincent Heuveline

Date Published: 18th Jul 2024

Publication Type: Journal

Finite element approximation of dielectrophoretic force driven flow problems

Abstract (Expand)

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 …f 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: Philipp Gerstner, Vincent Heuveline

Date Published: 1st May 2023

Publication Type: Journal

New Time Step Strategy for Multi-period Optimal Power Flow Problems

Abstract

Not specified

Authors: Nils Schween, Philipp Gerstner, Nico Meyer-Hübner, Vincent Heuveline

Date Published: 2021

Publication Type: InBook

Analysis and Numerical Approximation of Dielectrophoretic Force Driven Flow Problems

Abstract

Not specified

Author: Philipp Gerstner

Date Published: 11th Sep 2020

Publication Type: Doctoral Thesis

Dielectrophoretic force driven convection in annular geometry under Earth’s gravity

Abstract (Expand)

Context A radial temperature difference together with an inhomogeneous radial electric field gradient is applied to a dielectric fluid confined in a vertical cylindrical annulus inducing thermal … electro-hydrodynamic convection. Aims Identification of the stability of the flow and hence of the line of marginal stability separating stable laminar free (natural) convection from thermal electro-hydrodynamic convection, its flow structures, pattern formation and critical parameters. Methods Combination of different measurement techniques, namely the shadowgraph method and particle image velocimetry, as well as numerical simulation are used to qualify/quantify the flow. Results We identify the transition from stable laminar free convection to thermal electro-hydrodynamic convective flow in a wide range of Rayleigh number and electric potential. The line of marginal stability found confirms results from linear stability analysis. The flow after first transition forms a structure of axially aligned stationary columnar modes. We experimentally confirm critical parameters resulting from linear stability analysis and we show numerically an enhancement of heat transfer.

Authors: Torsten Seelig, Antoine Meyer, Philipp Gerstner, Martin Meier, Marcel Jongmanns, Martin Baumann, Vincent Heuveline, Christoph Egbers

Date Published: 1st Aug 2019

Publication Type: Journal

A time step reduction method for Multi-Period Optimal Power Flow problems

Abstract

Not specified

Authors: Nils Schween, Nico Meyer-Hübner, Philipp Gerstner, Vincent Heuveline

Date Published: 30th May 2019

Publication Type: Journal

Analysis of the Stationary Thermal-ElectroHydrodynamic Boussinesq Equations

Abstract

Not specified

Authors: Philipp Gerstner, Martin Baumann, Vincent Heuveline

Date Published: 14th Apr 2019

Publication Type: Journal

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