We consider solutions to the Navier-Stokes equations with Navier boundary conditions in a bounded domain Ω in R with a Cboundary Γ. Navier boundary conditions can be expressed in the form ω(v) = (2κ−α)v · τ and v ·n = 0 on Γ, where v is the velocity, ω(v) the vorticity, n a unit normal vector, τ a unit tangent vector, and α is in L∞(Γ). Such solutions have been considered in [2] and [3], and, i...

A boundary element method (BEM) combined with a linear slip boundary condition is proposed to calculate SH wave scattering from fractures. The linear slip boundary condition was proposed by Schoenberg (1980) to model elastic wave propagation through an imperfectly bonded interface, where the traction cross the interface is continuous and displacement is discontinuous. Here, we demonstrate how t...

In this work, I present the form of the Navier-Stokes equations implied by the Helmholtz decomposition in which the relation of the irrotational and rotational velocity fields is made explicit. The idea of self-equilibration of irrotational viscous stresses is introduced. The decomposition is constructed by first selecting the irrotational flow compatible with the flow boundaries and other pres...

mathematical model is developed for the time-dependent circular tube flow of compressible olymeric liquids subject to pressure-dependent slip at the wall and applied to a poly dimethyl iloxane PDMS . The parameters of pressure-dependent wall slip velocity and shear viscosity of he PDMS were determined using combinations of small-amplitude oscillatory shear, steady orsional and squeeze flows and...

Abstract   Due to restrictions on the choice of relaxation time in single relaxation time (SRT) models, simulation of flows is generally limited base on this method. In this paper, the SRT lattice Boltzmann equation was used to simulate lid driven cavity flow at different Reynolds numbers (100-5000) and three aspect ratios, K=1, 1.5 and 4. The point which is vital in convergence of this scheme ...

In the technique of microrheology, macroscopic rheological parameters as well as information about local structure are deduced from the behavior of microscopic probe particles under thermal or active forcing. Microrheology requires knowledge of the relation between macroscopic parameters and the force felt by a particle in response to displacements. We investigate this response function for a s...

How to properly specify boundary conditions for pressure is a longstanding problem for the incompressible Navier–Stokes equations with no-slip boundary conditions. An analytical resolution of this issue stems from a recently developed formula for the pressure in terms of the commutator of the Laplacian and Leray projection operators. Here we make use of this formula to (a) improve the accuracy ...

We consider slip with friction and penetration with resistance boundary conditions in the steady state Navier– Stokes equations. This paper describes some aspects of the implementation of these boundary conditions for /nite element discretizations. Numerical tests on twoand three-dimensional channel 2ows across a step using the slip with friction boundary condition study the in2uence of the fri...