| Issue |
Math. Model. Nat. Phenom.
Volume 18, 2023
|
|
|---|---|---|
| Article Number | 17 | |
| Number of page(s) | 34 | |
| Section | Mathematical methods | |
| DOI | https://doi.org/10.1051/mmnp/2023016 | |
| Published online | 01 August 2023 | |
Pressure boundary conditions for viscous flows in thin tube structures: Stokes equations with locally distributed Brinkman term
1 Institute Camille Jordan UMR CNRS 5208, University Jean Monnet, 23 rue P. Michelon, 42023, Saint-Etienne, France and Institute of Applied Mathematics, Vilnius University, Naugarduko Str. 24, Vilnius 03225, Lithuania.
2 Institute of Applied Mathematics, Vilnius University, Naugarduko Str. 24, Vilnius 03225, Lithuania.
* Corresponding author: grigory.panasenko@univ-st-etienne.fr
Received:
22
February
2023
Accepted:
10
May
2023
The steady state Stokes-Brinkman equations in a thin tube structure is considered. The Brinkman term differs from zero only in small balls near the ends of the tubes. The boundary conditions are: given pressure at the inflow and outflow of the tube structure and the no slip boundary condition on the lateral boundary. The complete asymptotic expansion of the problem is constructed. The error estimates are proved. The method of partial asymptotic dimension reduction is introduced for the Stokes-Brinkman equations and justified by an error estimate. This method approximates the main problem by a hybrid dimension problem for the Stokes-Brinkman equations in a reduced domain.
Mathematics Subject Classification: 35Q35 / 76D07
Key words: Navier-Stokes equations / Brinkman equations / Pressure boundary condition / Asymptotic approximation / Quasi-Poiseuille flows / Boundary layers
© The authors. Published by EDP Sciences, 2023
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