V European Conference on Computational Fluid Dynamics ECCOMAS CFD 2010 J. C. F. Pereira and A. Sequeira (Eds) Lisbon, Portugal,14-17 June 2010 MIMETIC SPECTRAL ELEMENT METHOD FOR GENERALIZED CONVECTION-DIFFUSION PROBLEMS J.J. Kreeft * , A. Palha † and M.I. Gerritsma † * Delft University of Technology, Faculty of Aerospace Engineering, Kluyverweg 2, 2629 HT Delft, The Netherlands e-mail: J.J.Kreeft@tudelft.nl † Delft University of Technology, Faculty of Aerospace Engineering, Kluyverweg 2, 2629 HT Delft, The Netherlands e-mail: {A.Palha,M.I.Gerritsma}@tudelft.nl Key words: Mimetic discretization, differential geometry, Spectral Element Method, convection-diffusion Abstract. In the last few decades geometrically-derived techniques to discretize partial differential equation encounter increasing popularity, because of their structure-preserving properties. These techniques make use of differential geometry to formulate the partial differential equations in continuous space and use algebraic topology as its discrete coun- terpart. In algebraic topology variables can be prescribed on different kinds of geometric objects, like points, lines, surfaces, volumes, but also space-time objects. Moreover differential geometry and algebraic topology lead to a representation that clearly separates the pure topological and the metric dependent part of the PDE and its discretization. Methods based on these principles are known as mimetic techniques, since they mimic the underlying geometric structures. The mimetic spectral element method presented is based on Lagrange and edge inter- polants that satisfy the mimetic properties and are able to reconstruct differential forms from cochains. The discretization is explained using a number of sample problems and some numerical examples are given to demonstrate the possibilities of the method presented. 1