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Spectral Element-FCT Method for the Compressible Euler Equations

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Part of the Notes on Numerical Fluid Mechanics (NNFM) book series (NNFM,volume 43)


A new algorithm based on spectral element discretizations and flux-corrected transport (FCT) concepts is developed for the solution of systems of hyperbolic conservation laws governing inviscid fluid flow. The current paper presents extensions to our previous work (see [6]) on scalar hyperbolic laws. A conservative formulation is proposed based on one-and two-dimensional cell-averaging and reconstruction procedures, which employ a stagerred mesh of Gauss-Chebyshev and Gauss-Lobatto-Chebyshev discretizations. Particular emphasis is placed on the construction of robust boundary and interfacial conditions in one- and two-dimensional domains. It is demonstrated through a shock-tube problem and a two-dimensional simulation of the compressible Euler equations that the proposed algorithm leads to stable, non-oscillatory solutions of high accuracy. In particular, in our model problems shocks are represented with at most two grid points, and expansion fans are represented very accurately. The spectral element-FCT method introduces minimum dispersion and diffusion errors as well as great flexibility in the discretization, since a variable number of macro-elements or collocation points per element can be employed to accomodate both accuracy and geometric requirements.

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© 1993 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden

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Giannakouros, J., Sidilkover, D., Karniadakis, G.E. (1993). Spectral Element-FCT Method for the Compressible Euler Equations. In: Donato, A., Oliveri, F. (eds) Nonlinear Hyperbolic Problems: Theoretical, Applied, and Computational Aspects. Notes on Numerical Fluid Mechanics (NNFM), vol 43. Vieweg+Teubner Verlag.

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  • Publisher Name: Vieweg+Teubner Verlag

  • Print ISBN: 978-3-528-07643-6

  • Online ISBN: 978-3-322-87871-7

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