Research Interests
My current research concerns the development, the analysis and the
application of finite volume methods to the numercial solution of
problems in electrochemistry, porous media flow and
photolithography. Questions of modeling, and of computer
implementations do concern me as well.
Finite Volume Method
Finite volume methods are successfully applied to a large range of
problems derived from conservation laws. The Voronoi box based finite
volume method for a convection-diffusion reaction problem in an
isotropic medium can be formulated using flux functions which describe
both convection and diffusion it was possible to use this
approach in order to generalize the Allen Southwell scheme to the
nonlinear case.
This type of formulation can be generalized to systems of equations.
It allows to decouple geometrical and problem specific information and
gives rise to the design of a programming interface where
implementations of new problems can be developed, focusing on the
problem specific part to be implemente in storage terms, reaction
terms, and flux functions.
Among the challenges for this method are anisotropy, efficient
algoritms for handling 3D problems, mass conservation in Navier Stokes
equations, coupling of Navier-Stokes equations and flow in porous
media.
Electrochemistry and FuelCells
Using the general approach
described above, we implemented and tested a numerical model of a Direct
Methanol Fuel Cell
which among other featueres includes two phase flow in porous media,
mass transport in a gas mixture, reaction kinetics with adsorbed
intermediates. Being rather complex, this model demonstrates the
potential available for numerical modeling in electrochemistry. The
mathematical and numerical analysis of subsets of this type of models
poses a number of interesting questions.
With respect to applications, current developments concern the
combination of the methods developed with methods impedance
spectroscopy (without equivalent circuit), tools for nonlinear
analysis of phenonena like bifurcation and chaos.
