Time‐dependent flow across a step: the slip with friction boundary condition

Abstract

SUMMARYThe paper studies numerically the slip with friction boundary condition in the time-dependent incompressible Navier-Stokes equations. Numerical tests on two-and three-dimensional channel ows across a step using this boundary condition on the bottom wall are performed. The in uence of the friction parameter on the ow ÿeld is studied and the results are explained according to the physics of the ow. Due to the stretching and tilting of vortices, the three-dimensional results di er in many respects from the two-dimensional ones.

Enabling numerical accuracy of Navier-Stokes-αthrough deconvolution and enhanced stability

“…The problem setup is similar to the 2D step, and is taken from [29]. The domain is a 10 × 40 × 10 rectangular box, with a step of height 1 and width 1 set at the bottom of the channel, starting 5 units in.…”

“…Since the model studied herein is in rotational form, the so-called do-nothing boundary condition (which corresponds to zero traction) is inappropriate, and so the advective boundary condition is used. As in [29], we use the steady NSE solution with Re = 20 as the initial condition, and compute to T = 20 using ν = 1/200, giving the Reynolds number Re = 200, using the size of the step for the length scale.…”

Continuity of Drag and Domain Stability in the Low Mach Number Limits

“…Recently, the possibility of liquid slippage along the boundary has been debated, in particular in connection with nano-technologies, see Priezjev and Troian [13]. The relevance of the slip condition for gases was discussed by Coron [3], John and Liakos [9], see also Málek and Rajagopal [12].…”

Mathematical Modelling of Glass Forming Processes

“…A commonly used boundary condition to describe fluid flow at an impenetrable wall [15,21,31,53] is Navier's slip condition: can be obtained by using the Tresca model [18]. Introduce a dimensionless friction coefficient,…”