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Algebraic Flux Correction II. Compressible Euler Equations

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Book cover Flux-Corrected Transport

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

Summary

Algebraic flux correction schemes of TVD and FCT type are extended to systems of hyperbolic conservation laws. The group finite element formulation is employed for the treatment of the compressible Euler equations. An efficient algorithm is proposed for the edge-by-edge matrix assembly. A generalization of Roe’s approximate Riemann solver is derived by rendering all off-diagonal matrix blocks positive semi-definite. Another usable low-order method is constructed by adding scalar artificial viscosity proportional to the spectral radius of the cumulative Roe matrix. The limiting of antidiffusive fluxes is performed using a transformation to the characteristic variables or a suitable synchronization of correction factors for the conservative ones. The outer defect correction loop is equipped with a block-diagonal preconditioner so as to decouple the discretized Euler equations and solve them in a segregated fashion. As an alternative, a strongly coupled solution strategy (global BiCGSTAB method with a block-Gauß-Seidel preconditioner) is introduced for applications which call for the use of large time steps. Various algorithmic aspects including the implementation of characteristic boundary conditions are addressed. Simulation results are presented for inviscid flows in a wide range of Mach numbers.

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Authors and Affiliations

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

    Dmitri Kuzmin

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  1. Dmitri Kuzmin
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  2. Matthias Möller
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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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Kuzmin, D., Möller, M. (2005). Algebraic Flux Correction II. Compressible Euler Equations. 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_7

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