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## Rigorous justification of the Kirchoff law for junction of thin pipes filled with viscous fluid

Marušić-Paloka, Eduard
Rigorous justification of the Kirchoff law for junction of thin pipes filled with viscous fluid // Asymptotic Analysis, 33 (2003), 1; 51-66 (međunarodna recenzija, članak, znanstveni)

Naslov
Rigorous justification of the Kirchoff law for junction of thin pipes filled with viscous fluid

Autori
Marušić-Paloka, Eduard

Izvornik
Asymptotic Analysis (0921-7134) 33 (2003), 1; 51-66

Ključne riječi
Thin pipes; Navier-Stokes equations; Poiseuille flow; junction; Leray problem.

Sažetak
We study the junction of $m$ pipes that are either thin or long (i.e. they have small ratio between the cross-section and the length, denoted by $\varepsilon$). Pipes are filled with incompressible Newtonian fluid and the values of the pressure $p_i$ at the end of each pipe are prescribed. By rigorous asymptotic analysis, as $\varepsilon\to 0$, we justify the analog of the Kirchhoff law for computing the junction pressure. In interior of each pipe the effective flow is the Poiseuille flow governed by the pressure drop between the end of the pipe and the junction point. The pressure at the junction point is equal to a weighted mean value of the prescribed $p_i$-s (Kirchhoff law). In the vicinity of the junction there is an interior layer, with thickness $\varepsilon\, \mbox{; ; ; ; log}; ; ; ; (1/\varepsilon)$. To get a better approximation and to control the velocity gradient in vicinity of the junction, first order asymptotic approximation has to be corrected by solving the appropriate Leray problem. We prove the asymptotic error estimate for the approximation.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

Projekt / tema
0037116

Ustanove
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb

Profili:

Eduard Marušić-Paloka (autor)

#### Citiraj ovu publikaciju

Marušić-Paloka, Eduard
Rigorous justification of the Kirchoff law for junction of thin pipes filled with viscous fluid // Asymptotic Analysis, 33 (2003), 1; 51-66 (međunarodna recenzija, članak, znanstveni)
Marušić-Paloka, E. (2003) Rigorous justification of the Kirchoff law for junction of thin pipes filled with viscous fluid. Asymptotic Analysis, 33 (1), 51-66.
@article{article, author = {Maru\v{s}i\'{c}-Paloka, E.}, year = {2003}, pages = {51-66}, keywords = {Thin pipes, Navier-Stokes equations, Poiseuille flow, junction, Leray problem.}, journal = {Asymptotic Analysis}, volume = {33}, number = {1}, issn = {0921-7134}, title = {Rigorous justification of the Kirchoff law for junction of thin pipes filled with viscous fluid}, keyword = {Thin pipes, Navier-Stokes equations, Poiseuille flow, junction, Leray problem.} }

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