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Quantifier elimination supported proofs in the numerical treatment of fluid flows

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

During the analysis of numerical methods for fluid flows some properties of numerical methods as stability or monotonicity can be stated as quantified problems and proved by quantifier elimination. A case study demonstrating such proofs is presented. The study shows that the stability region of the central scheme for advection-diffusion equation with Runge–Kutta time discretization is much bigger than classical stability region.

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Authors and Affiliations

  1. Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Brehova 7, 115 19, Prague 1, Czech Republic

    Richard Liska & Pavel Váchal

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  1. Richard Liska
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  2. Pavel Váchal
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Correspondence to Richard Liska.

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This work was supported in part by the Czech Ministry of Education projects MSM 6840770010 and LC06052.

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Liska, R., Váchal, P. Quantifier elimination supported proofs in the numerical treatment of fluid flows. AAECC 18, 575–582 (2007). https://doi.org/10.1007/s00200-007-0057-6

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  • DOI: https://doi.org/10.1007/s00200-007-0057-6

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