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Flux-Corrected Transport pp 251–296Cite as

Algebraic Flux Correction III. Incompressible Flow Problems

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

Summary

Algebraic FEM-FCT and FEM-TVD schemes are integrated into incompressible flow solvers based on the ‘Multilevel Pressure Schur Complement’ (MPSC) approach. It is shown that algebraic flux correction is feasible for nonconforming (rotated bilinear) finite element approximations on unstructured meshes. Both (approximate) operator-splitting and fully coupled solution strategies are introduced for the discretized Navier-Stokes equations. The need for development of robust and efficient iterative solvers (outer Newton-like schemes, linear multigrid techniques, optimal smoothers/preconditioners) for implicit high-resolution schemes is emphasized. Numerical treatment of extensions (Boussinesq approximation, Κ — ε turbulence model) is addressed and pertinent implementation details are given. Simulation results are presented for three-dimensional benchmark problems as well as for prototypical applications including multiphase and granular flows.

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Authors and Affiliations

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

    Stefan Turek

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  1. Stefan Turek
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  2. Dmitri Kuzmin
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Editors and Affiliations

  1. Department of Mathematics, University of Dortmund, LS III, Vogelpothsweg 87, 44227, Dortmund, Germany

    Dmitri Kuzmin  & Stefan Turek  & 

  2. School of Computational Sciences, George Mason University, Chain Bridge Road, 103 4260, Fairfax, Virginia, 22030-4444, USA

    Rainald Löhner

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Turek, S., Kuzmin, D. (2005). Algebraic Flux Correction III. Incompressible Flow Problems. In: Kuzmin, D., Löhner, R., Turek, S. (eds) Flux-Corrected Transport. Scientific Computation. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27206-2_8

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