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The coupling system of Navier–Stokes equations and elastic Navier–Lame equations in a blood vessel
Author(s) -
Liu Demin,
Li Linjin
Publication year - 2020
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22464
Subject(s) - finite element method , mathematics , navier–stokes equations , cylinder , coordinate system , mathematical analysis , cylindrical coordinate system , system of linear equations , shell (structure) , coupling (piping) , geometry , mechanics , compressibility , physics , mechanical engineering , materials science , engineering , composite material , thermodynamics
In this paper, the blood flow problem is considered in a blood vessel, and a coupling system of Navier–Stokes equations and linear elastic equations, Navier–Lame equations, in a cylinder with cylindrical elastic shell is given as the governing equations of the problem. We provide two finite element models to simulating the three‐dimensional Navier–Stokes equations in the cylinder while the asymptotic expansion method is used to solving the linearly elastic shell equations. Specifically, in order to discrete the Navier–Stokes equations, the dimensional splitting strategy is constructed under the cylinder coordinate system. The spectral method is adopted along the rotation direction while the finite element method is used along the other directions. By using the above strategy, we get a series of two‐dimensional‐three‐components (2D‐3C) fluid problems. By introduce the S‐coordinate system in E 3 and employ the thickness of blood vessel wall as the expanding parameter, the asymptotic expansion method can be established to approximate the solution of the 3D elastic problem. The interface contact conditions can be treated exactly based on the knowledge of tensor analysis. Finally, numerical test shows that our method is reasonable.