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Modelling of solid oxide fuel cells


A mathematical model of a SOFC (solid oxide fuel cell) is a system of partial differential equations in a moderately complicated geometry with nonlinear couplings. The single equations describe the fields of temperature, voltage and concentrations of gases. From physics it is clear that neither existance nor uniqueness of a solution can be expected for arbitrary choices of operating conditions and material data.

The equations are discretised using the FIT method. The discretised equations are solved by a full multigrid method. The nonlinear coupling is handled mostly on the fine grid level, but for the coupling of concentration and voltage in the electrochemical kinetics, a treatment in an inner loop is possible, too. The grid is planned to consist of triangular as well as rectangular cells.


In the end the project shall lead to a user-friendly program for geometry design of fuel cells. An efficient discretization shall be achieved consisting of FIT-regular i.e. non-obtused grid cells. In addition a modelling program for the mass, flows and temperatures will be developed. The modelling allows a rapid and detailed testing of designs for SOFC.

Partners / Grants

  • Institute for Energy Processing Techniques, Forschungszentrum Jülich
  • Central Institute for Applied Mathematics (ZAM), Forschungszentrum Jülich

The project was funded by the German Federal Ministry of Education and Research (BMBF).

The grant period was October 1993 until December 1996.

Status and Results

The project was finished in schedule.

The describing field equations were discretized using the FIT method (Finite Integration Technique). For the solution of the emerging non-linearities, two different models were developed, one for the reaction dominated case of normal operation, the other for the transport bounded case. To handle different cell geometries, an interactive construction of an irregular grid for the FIT discretization was designed.

The developed and implemented programs allow for the SOFC the modelling of the full spectrum of working conditions, from idling until short circuit, for different geometries and fuel mixtures. Additionally, two variants werde developed for the internal methane reforming and for the impedance calculation of a calibration SOFC with reference electrode.


  • Hochauflösende Modellierung von SOFC-Brennstoffzellen
    Schelthoff, Ch.; Steffen, B. (1995)
    Technical Report KFA-ZAM-IB-9521
  • Modellierung und Simulation am Beispiel von Hochtemperatur-Brennstoffzellen
    Schelthoff, Ch.; Steffen, B. (1996)
    PIK - Praxis der Informationsverarbeitung und Kommunikation 3/96, S.138-141
  • Hochauflösende Modellierung von SOFC-Brennstoffzellen
    Schelthoff, Ch. et al.(1997)
    Springer, Sonderband zum Statusseminar der BMBF-Verbundprojekte, S. 105-115 (1997)
  • Modellierung der SOFC-Brennstoffzelle und die numerische Lösung mit einem adaptiven Full-Multigrid-Verfahren
    Schelthoff, Ch. (1997)
    Bericht des Forschungszentrums Jülich; Jül-3380, ISSN 0944-2952 (Diss. Universität Gießen 1997)
  • Hochauflösende Modellierung von SOFC-Brennstoffzellen
    Schelthoff, Ch.; Steffen, B.; Weidner, P.; Hoßfeld, F. (1997)
    Poster zur BMBF-Statustagung, Oktober 1997