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Numerical solution of the viscous flows in a network of thin tubes: equations on the graph

Abstract : A non-stationary flow in a network of thin tubes is considered. Its one-dimensional approximation was proposed in a paper by G.Panasenko and K.Pileckas, Flows in a tube structure: equation on the graph, JMP (2014). It consists of a set of equations with weakly singular kernels, on a graph, for the macroscopic pressure. A new difference scheme for this problem is proposed. Several variants are discussed. Stability and convergence are carefully investigated , theoretically and numerically. In addition, numerical results are compared to the direct numerical solution of the full dimension Navier-Stokes equations.
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https://hal.archives-ouvertes.fr/hal-02407080
Contributor : Frédéric Chardard <>
Submitted on : Thursday, December 12, 2019 - 12:55:07 PM
Last modification on : Wednesday, July 8, 2020 - 12:44:00 PM
Document(s) archivé(s) le : Friday, March 13, 2020 - 9:23:02 PM

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  • HAL Id : hal-02407080, version 1

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Éric Canon, Frédéric Chardard, Grigory Panasenko, Olga Štikonienė. Numerical solution of the viscous flows in a network of thin tubes: equations on the graph. 2019. ⟨hal-02407080⟩

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