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Implicit FEM-FCT algorithm for compressible flows

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • Matthias Möller

    (University of Dortmund, Institute of Applied Mathematics (LSIII))

  • Dmitri Kuzmin

    (University of Dortmund, Institute of Applied Mathematics (LSIII))

  • Stefan Turek

    (University of Dortmund, Institute of Applied Mathematics (LSIII))

Abstract

Summary The flux-corrected transport (FCT) methodology is generalized to implicit finite element schemes and applied to the Euler equations of gas dynamics. The underlying low-order scheme is constructed by applying scalar artificial viscosity proportional to the spectral radius of the cumulative Roe matrix. All conservative matrix manipulations are performed edge-by-edge which leads to an efficient algorithm for the matrix assembly. The outer defect correction loop is equipped with a block-diagonal preconditioner so as to decouple the discretized Euler equations and solve all equations individually. As an alternative, a strongly coupled solution strategy is investigated in the context of stationary problems which call for large time steps.

Suggested Citation

  • Matthias Möller & Dmitri Kuzmin & Stefan Turek, 2004. "Implicit FEM-FCT algorithm for compressible flows," Springer Books, in: Miloslav Feistauer & Vít Dolejší & Petr Knobloch & Karel Najzar (ed.), Numerical Mathematics and Advanced Applications, pages 641-650, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18775-9_62
    DOI: 10.1007/978-3-642-18775-9_62
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