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

Éric Canon (1, 2) , Frédéric Chardard (1, 2) , Grigory Panasenko (2, 1) , Olga Štikonienė (3)

1 MMCS - Modélisation mathématique, calcul scientifique
2 ICJ - Institut Camille Jordan
3 Department of Mathematics and Informatics [Vilnius]

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.

Mots clés: Navier-Stokes equations; asymptotic models; weakly singular kernels; 78M35; 74G10; 35Q30; 35R09; 34K28; multi-scale problems

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]; Mécanique des fluides [physics.class-ph]

Éric Canon, Frédéric Chardard, Grigory Panasenko, Olga Štikonienė. Numerical solution of the viscous flows in a network of thin tubes: equations on the graph. Journal of Computational Physics, 2021, 435, pp.110262. ⟨10.1016/j.jcp.2021.110262⟩. ⟨hal-02407080⟩