Hauptseminar Porous Media SS 2021/Reaction diffusion advection with FEM

Date

2021-06-18

Time

15:30

Topic

Reaction-diffusion-advection systems with finite elements

Speaker

Kristin Lorenz

Tutor

Patrick Kreissl

Contents

The Finite Element Method (FEM) is a computational technique that can be used to solve coupled systems of (non-linear) partial differential equation (PDEs) numerically. A key aspect of this method is the discretization of a large simulation domain into smaller, so-called finite elements over which the solution to the respective PDE can be well approximated. Refining the mesh locally in the regions of the simulation domain that are critical for the physical effects (charged walls, in-/outflow regions, catalyst regions consuming/producing chemical species, …), this typically allows one to study systems on an experimental length scale, even for setups with complex geometries. Obviously, this makes FEM also an interesting tool for the simulation of porous systems.

This talk will introduce FEM and show how the method can be used to solve the reaction–diffusion–advection equations. To illustrate this, an example system will be presented, namely a microfluidic pump based a ion-exchange-resin in a slit-pore geometry.

Literature

• Sascha Ehrhardt.
  Simulation of Electroosmotic Flow through Nanocapillaries using Finite-Element Methods.
  Master's thesis, University of Stuttgart, 2016.
  [PDF] (11 MB)
• Georg Rempfer, Gary B. Davies, Christian Holm, Joost de Graaf.
  Reducing spurious flow in simulations of electrokinetic phenomena.
  The Journal of Chemical Physics 145(4):044901, 2016.
  [PDF] (3.1 MB) [DOI]
• Ran Niu, Patrick Kreissl, Aidan Thomas Brown, Georg Rempfer, Denis Botin, Christian Holm, Thomas Palberg, Joost de Graaf.
  Microfluidic pumping by micromolar salt concentrations.
  Soft Matter 13(7):1505–1518, 2017.
  [PDF] (4.5 MB) [DOI]