scholarly journals Outflow boundary conditions for the incompressible non-homogeneous Navier-Stokes equations

2007 ◽  
Vol 7 (2) ◽  
pp. 219-250 ◽  
Author(s):  
Franck Boyer ◽  
◽  
Pierre Fabrie ◽  
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Outflow Boundary Conditions ◽  
Outflow Boundary

scholarly journals Steady-State Navier–Stokes Equations in Thin Tube Structure with the Bernoulli Pressure Inflow Boundary Conditions: Asymptotic Analysis

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2433
Author(s):  
Rita Juodagalvytė ◽  
Grigory Panasenko ◽  
Konstantinas Pileckas
Keyword(s):  
Weak Solution ◽  
Steady State ◽  
Boundary Conditions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Thin Tube ◽  
Outflow Boundary ◽  
Tube Structure

Steady-state Navier–Stokes equations in a thin tube structure with the Bernoulli pressure inflow–outflow boundary conditions and no-slip boundary conditions at the lateral boundary are considered. Applying the Leray–Schauder fixed point theorem, we prove the existence and uniqueness of a weak solution. An asymptotic approximation of a weak solution is constructed and justified by an error estimate.

scholarly journals Downstream-Conditioned Maximum Entropy Method for Exit Boundary Conditions in the Lattice Boltzmann Method

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Javier A. Dottori ◽  
Gustavo A. Boroni ◽  
Alejandro Clausse
Keyword(s):  
Boundary Conditions ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Entropy Method ◽  
Alternative Methods ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Outflow Boundary ◽  
Boltzmann Method

A method for modeling outflow boundary conditions in the lattice Boltzmann method (LBM) based on the maximization of the local entropy is presented. The maximization procedure is constrained by macroscopic values and downstream components. The method is applied to fully developed boundary conditions of the Navier-Stokes equations in rectangular channels. Comparisons are made with other alternative methods. In addition, the new downstream-conditioned entropy is studied and it was found that there is a correlation with the velocity gradient during the flow development.

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