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Pré-Publication, Document De Travail Année : 2020

Numerical solution of viscous flows in a network of thin tubes: asymptotics and discretization in the cross-section

Résumé

Previously, we considered numerics for a problem on a connected 1D-graph obtained by Panasenko and Pileckas, as the limit model of nonsteady Navier-Stokes equations in a tube structure. The problem is described by nonlocal in time diffusion equations, where weakly singular convolution kernels arise. These kernels are obtained from the heat equation on the cross-sections of the tubes. Their properties and discretization are the topic of the present paper. First, the existence of asymptotic expansions for small times is proved, with explicit formula (with respect to the geometry of the cross-section) for the first five terms. Then, as direct discretization of the equations for the kernels leads to poor approximations due to lack of regularity, numerical schemes that use these asymptotics for small times are designed. Convergence theorems are proved with estimations on the order of convergence. Numerical experiments highlight the interest of this correction.
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Dates et versions

hal-02906473 , version 1 (24-07-2020)
hal-02906473 , version 2 (22-12-2021)
hal-02906473 , version 3 (14-01-2022)
hal-02906473 , version 4 (29-07-2023)

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  • HAL Id : hal-02906473 , version 1

Citer

Éric Canon, Frédéric Chardard, Grigory Panasenko, Olga Štikonienė. Numerical solution of viscous flows in a network of thin tubes: asymptotics and discretization in the cross-section. 2020. ⟨hal-02906473v1⟩
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