76 research outputs found
On the Roughness-Induced Effective Boundary Conditions for an Incompressible Viscous Flow
AbstractWe consider the laminar viscous channel flow with the lateral surface of the channel containing surface irregularities. It is supposed that a uniform pressure gradient is maintained in the longitudinal direction of the channel. After studying the corresponding boundary layers, we obtain rigorously the Navier friction condition. It is valid when the size and amplitude of the imperfections tend to zero. Furthermore, the coefficient in the law is determined through an auxiliary boundary-layer type problem, and the tangential drag force and the effective mass flow are determined up to order O(ε3/2). The value of the effective coefficient is shown to be independent with respect to the position of the mean surface in the range of O(ε)
Pressure jump interface law for the Stokes-Darcy coupling: Confirmation by direct numerical simulations
It is generally accepted that the effective velocity of a viscous flow over a
porous bed satisfies the Beavers-Joseph slip law. To the contrary, interface
law for the effective stress has been a subject of controversy. Recently, a
pressure jump interface law has been rigorously derived by Marciniak-Czochra
and Mikeli\'c. In this paper, we provide a confirmation of the analytical
result using direct numerical simulation of the flow at the microscopic level.Comment: 25 pages, preprin
Effective pressure interface law for transport phenomena between an unconfined fluid and a porous medium using homogenization
We present modeling of the incompressible viscous flows in the domain
containing an unconfined fluid and a porous medium. For such setting a rigorous
derivation of the Beavers-Joseph-Saffman interface condition was undertaken by
J\"ager and Mikeli\'c [SIAM J. Appl. Math. \rm 60 (2000), p. 1111-1127] using
the homogenization method. So far the interface law for the pressure was
conceived and confirmed only numerically. In this article we justify rigorously
the pressure jump condition using the corresponding boundary layer
Global-in-time solutions for the isothermal Matovich-Pearson equations
In this paper we study the Matovich-Pearson equations describing the process
of glass fiber drawing. These equations may be viewed as a 1D-reduction of the
incompressible Navier-Stokes equations including free boundary, valid for the
drawing of a long and thin glass fiber. We concentrate on the isothermal case
without surface tension. Then the Matovich-Pearson equations represent a
nonlinearly coupled system of an elliptic equation for the axial velocity and a
hyperbolic transport equation for the fluid cross-sectional area. We first
prove existence of a local solution, and, after constructing appropriate
barrier functions, we deduce that the fluid radius is always strictly positive
and that the local solution remains in the same regularity class. To the best
of our knowledge, this is the first global existence and uniqueness result for
this important system of equations
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