The research network "Coupled Flow Processes in Energy and Environmental Research" has been established 2008 - 2010 as the result of a successful joint proposal in the framework of the competitive procedure of the Leibniz Association within the "Joint Initiative for Research and Innovation" launched in 2005 by the German Federal Ministry for Education and Research.
Partners are:
- Weierstrass Institute for Applied Analysis and Stochastics, Head (and co-ordinator of the network): Dr. Jürgen Fuhrmann
- Potsdam Institute for Climate Impact Research, Head: Dr. Uwe Böhm
- Freie Universität Berlin, Heads: Prof. Dr. Rupert Klein & Prof. Dr. Ralf Kornhuber
- Friedrich-Alexander-Universität Erlangen-Nürnberg, Head: Prof. Dr. Eberhard Bänsch
The
research network aims at the establishment of effective cooperations
between national and international experts coming from universities and
different members of the Leibniz Scientific Community. Fundamental
contributions to the appropriate numerical treatment of coupled flow
problems are aspired, and will be put to the test by working on common
applications, where interdisciplinary knowledge is needed.
The WIAS researchers of the research network were in the Leibniz group 1 summarized. On the recommendation of Evaluation Commision, the work in the Research Group 3 continued.
Modeling of coupled flow processes
is an urgent and largely unsolved interdisciplinary problem. They have
eminent importance in energy research, geosciences, environmental and
climate research, civil engineering and materials science.
Common topics of the network:
- reactive transport of dissolved species
- interaction between free flow and flow in porous media
- exchange processes in multi-phase flows
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Mathematical models:
- free flow: (incompressible) Navier-Stokes equations
- porous media flow: Darcy and Brinkman model
- soil hydrology: (stochastic) Richards equation
- species transport: reaction-diffusion-convection equation
- interface conditions: boundary layer theory, Beavers-Joseph, ...
- flow and transport processes in fuel cells
- estimation of the impact of near-surface hydrological processes on the regional climate
Leibniz group 1
The focus of the Leibniz group 1 is on:- Numerical analysis: Discretization schemes for the Navier-Stokes equation on unstructured grids which preserve qualititive mathematical properties of the continuous model
- Modelling: interface conditions between free flow and porous media flow
The discretization
of species transport and reaction phenomena in coupled flow processes
is a challenging and urgent problem, since they arise in many
applications like energy research, and environmental sciences. Species
transport and reaction phenomena are modeled by systems of coupled
reaction-convection-diffusion equations. Their discretization with
classical vertex-based finite volume methods
on boundary-conforming Delaunay grids leads to discrete nonlinear equations with similar qualitative properties as the original continuous equations, e.g.,
- a local maximum principle and
- positivity.
While the appropriate discrete coupling of porous media flow
obeying Darcy's law with reaction-convection-diffusion
equations is well-understood within the finite-volume framework, the
appropriate discretization of flow processes obeying the incompressible
Stokes or Navier-Stokes equations is more involved. It turns out that
discrete incompressible flows have to fulfill a special notion of
discrete finite volume incompressibility, in order to
maintain discrete maximum principles and discrete positivity
of coupled species. We construct discrete incompressible flows
fulfilling these preconditions, either by
- using appropriate projections of classical flow discretizations like, e.g., FE methods or
- an appropriate direct discretization of the flow equations by edge-based finite volume methods.
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Additional challenges for an appropriate modeling of coupled flow processes arise, when porous media flows and flows obeying the Stokes and Navier-Stokes equations occur together in different parts of the underlying domain. Then, appropriate boundary conditions for the transition interface between the porous medium and the free flow region have to be used, e.g., the Beavers-Joseph condition.
Aims
Simulation of flow cell experiments in electrochemistry:
The Darcy and Navier-Stokes equations are coupled with a
convection-diffuson equation for the species transport by the
convective flux.
Electro-convective
instability and electro-dialysis:
The Nernst-Planck-Poisson
equations are
coupled with the Stokes or Navier-Stokes equations by the convective
flux and by the momentum transfer from the moving ions onto the fluid
particles.
The Leibniz group takes part in the following main application area: