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Algebraic Flux Correction III

Incompressible Flow Problems

  • Chapter
Flux-Corrected Transport

Part of the book series: Scientific Computation ((SCIENTCOMP))

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Abstract

This chapter illustrates the use of algebraic flux correction in the context of finite element methods for the incompressible Navier-Stokes equations and related models. In the convection-dominated flow regime, nonlinear stability is enforced using algebraic flux correction. The numerical treatment of the incompressibility constraint is based on the ‘Multilevel Pressure Schur Complement’ (MPSC) approach. This class of iterative methods for discrete saddle-point problems unites fractional-step/operator-splitting methods and strongly coupled solution techniques. The implementation of implicit high-resolution schemes for incompressible flow problems requires the use of efficient Newton-like methods and optimized multigrid solvers for linear systems. The coupling of the Navier-Stokes system with scalar conservation laws is also discussed in this chapter. The applications to be considered include the Boussinesq model of natural convection, the k–ε turbulence model, population balance equations for disperse two-phase flows, and level set methods for free interfaces. A brief description of the numerical algorithm is given for each problem.

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Acknowledgements

The authors would like to thank Shu-Ren Hysing, Otto Mierka, and Evren Bayraktar (TU Dortmund) for contributing their results. The collaboration with Prof. Peter Walzel (TU Dortmund) and Sulzer Chemtech Ltd is gratefully acknowledged.

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  1. Institute of Applied Mathematics (LS III), TU Dortmund, Vogelpothsweg 87, 44227, Dortmund, Germany

    Stefan Turek

  2. Applied Mathematics III, University Erlangen-Nuremberg, Cauerstr. 11, 91058, Erlangen, Germany

    Dmitri Kuzmin

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  1. , Chair of Applied Mathematics III, University of Erlangen-Nuremberg, Haberstr. 2, Erlangen, 91058, Germany

    Dmitri Kuzmin

  2. , School of Computational Sciences, George Mason University, 4400 University Drive MS 6A2, Fairfax, 22030, Virginia, USA

    Rainald Löhner

  3. Institute of Applied Mathematics, LS III, Dortmund University of Technology, Vogelpothsweg 87, Dortmund, 44227, Germany

    Stefan Turek

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Turek, S., Kuzmin, D. (2012). Algebraic Flux Correction III. In: Kuzmin, D., Löhner, R., Turek, S. (eds) Flux-Corrected Transport. Scientific Computation. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4038-9_8

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