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Higher Order Galerkin Time Discretization for Nonstationary Incompressible Flow

In: Numerical Mathematics and Advanced Applications 2011

Author

Listed:
  • S. Hussain

    (Institut für Angewandte Mathematik, TU-Dortmund)

  • F. Schieweck

    (Otto-von-Guericke-Universität Magdeburg, Institut für Analysis und Numerik)

  • S. Turek

    (Institut für Angewandte Mathematik, TU-Dortmund)

Abstract

In this paper, we extend our work for the heat equation in (Hussain et al., J Numer Math 19(1):41–61, 2011) and for the Stokes equations in (Hussain et al., Open Numer Methods J 4:35–45, 2012) to the nonstationary Navier-Stokes equations in two dimensions. We examine continuous Galerkin-Petrov (cGP) time discretization schemes for nonstationary incompressible flow. In particular, we implement and analyze numerically the higher order cGP(2)-method. For the space discretization, we use the LBB-stable finite element pair $$Q_{2}/P_{1}^{\mathit{disc}}$$ . The discretized systems of nonlinear equations are treated by using the fixed-point as well as the Newton method and the associated linear subproblems are solved by using a monolithic multigrid solver with GMRES method as smoother. We perform nonstationary simulations for a benchmarking configuration to analyze the temporal accuracy and efficiency of the presented time discretization scheme.

Suggested Citation

  • S. Hussain & F. Schieweck & S. Turek, 2013. "Higher Order Galerkin Time Discretization for Nonstationary Incompressible Flow," Springer Books, in: Andrea Cangiani & Ruslan L. Davidchack & Emmanuil Georgoulis & Alexander N. Gorban & Jeremy Levesley (ed.), Numerical Mathematics and Advanced Applications 2011, edition 127, pages 509-517, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-33134-3_54
    DOI: 10.1007/978-3-642-33134-3_54
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