Perspectives for rechargeable Mg/air batteries
Subproject: Macroscopic modeling of transport and reaction processes in magnesium-air-batteriesProject Head: Dr. Jürgen Fuhrmann, Prof. Dr. Helmut Baltruschat (Uni Bonn)
Research Assistants: Dr. Christian Merdon
Project Description
The project aims at the development of macroscopic models for coupled flow and reaction processes in magnesium air batteries and in experimental electochemical cells to investigate its components. On this basis numerical simulation tools are developed to run calculations that support the experiments performed within the joint research project. The development of models and the simulations shall facilitate a deeper understanding of subprocesses and their interrelationship.
Divergence-free coupling of Navier-Stokes and Tranport Equations
The divergence-constraint is a key ingredient for physically correct behaviour of the coupled system. To ensure the mass conservation of the velocity that enters in the finite volume discretisation of the transport equation, a novel modified Crouzeix-Raviart finite element method for the Navier-Stokes equations based on [1] was investigated. The modification concerns a reconstruction of the discrete divergence-free test functions onto divergence-free Raviart-Thomas functions. This modification ensures optimal pressure-independent a priori energy error estimates and the preservation of the maximum principle in the coupling. Extensions to higher-order finite element methods are possible [2] and can lead to significant improvements for problems with complicated pressures [3].
Example 1: Concentration field in a flow through an U-shaped domain| Flow calculation with standard nonconforming Crouzeix-Raviart FEM without reconstructions violates the maximum principle | Flow calculation with nonconforming Crouzeix-Raviart-FEM with Raviart-Thomas reconstructions of the test functions preserves the maximum principle |
References
[1] A. Linke, On the Role of the Helmholtz-Decomposition in Mixed Methods for Incompressible Flows and a New Variational Crime, Computer Methods in Applied Mechanics and Engineering, Vol. 268 (2014), pp. 782-800[2] A. Linke, G. Matthies, L. Tobiska, Robust arbitrary order mixed finite element methods for the incompressible Stokes equations with pressure independent velocity errors, ESAIM: Mathematical Modelling and Numerical Analysis, in press
[3] A. Linke, C. Merdon, On spurious oscillations due to irrotational forces in the Navier--Stokes momentum balance, WIAS Preprint No. 2132, (2015)
Links
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Energy Storage Funding Initiative |
Publications
Articles
| [4] | J. Fuhrmann, Comparison and numerical treatment of generalized Nernst-Planck Models, (accepted by Computer Physics Communications) WIAS Preprint No. 1940, (2014) |
| [3] | A. Linke and C. Merdon, Guaranteed energy error estimators for a modified robust Crouzeix-Raviart Stokes element, (accepted by Journal of Scientific Computing), WIAS Preprint No. 1979, (2014) |
| [2] | C. Brennecke, A. Linke, C. Merdon, J. Schöberl, Optimal and pressure-independent L^2 velocity error estimates for a modified Crouzeix-Raviart Stokes element with BDM reconstructions, J. Comput. Math. 33 (2015), no. 2, WIAS Preprint No. 1929 |
| [1] | J. Fuhrmann, A. Linke, C. Merdon, Coupling of Fluid Flow and Solute Transport Using a Divergence-Free Reconstruction of the Crouzeix-Raviart Element, FVCA 7, Finite Volumes for Complex Applications VII, Berlin, June 15-20, 2014, Springer Proceedings in Mathematics & Statistics, 587--595 |
Preprints
| [P6] | H. Baltruschat, J. Fuhrmann, M. Khodayari, A. Linke, C. Merdon, F. Neumann and T. Streckenbach, Inverse modeling of thin layer flow cells for detection of solubility, transport and reaction coefficients from experimental data, WIAS Preprint No. 2161, (2015) |
| [P5] | A. Linke, C. Merdon and W. Wollner, Optimal L2 velocity error estimate for a modified pressure-robust Crouzeix--Raviart Stokes element, WIAS Preprint No. 2140, (2015) |
| [P4] | A. Linke and C. Merdon, On spurious oscillations due to irrotational forces in the Navier--Stokes momentum balance, WIAS Preprint No. 2132, (2015) |
| [P3] | A. Linke and C. Merdon, Guaranteed energy error estimators for a modified robust Crouzeix-Raviart Stokes element, WIAS Preprint No. 1979, (2014) |
| [P2] | J. Fuhrmann, Comparison and numerical treatment of generalized Nernst-Planck Models, WIAS Preprint No. 1940, (2014) |
| [P1] | C. Brennecke, A. Linke, C. Merdon, J. Schöberl, Optimal and pressure-independent L^2 velocity error estimates for a modified Crouzeix-Raviart Stokes element with BDM reconstructions, WIAS Preprint No. 1929, (2014) |
Talks
| [2] | C. Merdon, A Modified Pressure-Robust 2nd-Order Finite Element Method for Navier-Stokes Discretisations, 28th FEM-Symposium, Chemnitz (2015-09-28) |
| [1] | C. Merdon, Inverse modeling of thin layer flow cells for detection of solubility, transport and reaction coefficients from experimental data, 17th Topical Meeting of the International Society of Electrochemistry in Saint-Malo, France (2015-06-01) |
Posters
| [Po4] | J. Fuhrmann, C. Merdon, Activity based finite volume methods for generalised Nernst-Planck-Poisson systems, ISE Lausanne (2014-09-03), (pdf coming soon) |
| [Po3] | J. Fuhrmann, A. Linke, C. Merdon, M. Khodayari, H. Baltruschat, Detection of Solubility, Transport and Reaction Coefficients from Experimental Data by Inverse Modeling of Thin Layer Flow Cells, ISE Lausanne (2014-09-03), (pdf coming soon) |
| [Po2] | J. Fuhrmann, Activity based finite volume methods for generalised Nernst-Planck-Poisson systems, FVCA7 Berlin (2014-06-19), >>PDF<< |
| [Po1] | J. Fuhrmann, A. Linke, C. Merdon, Coupling of Fluid Flow and Solute Transport Using a Divergence-Free Reconstruction of the Crouzeix-Raviart Element, FVCA7 Berlin (2014-06-17), >>PDF<< |