The prediction of spatially periodic flows using a finite‐volume model

Abstract

SUMMARYA periodic boundary condition has been developed that can be used in conjunction with a speciÿed ow rate to produce accurate results in spatially periodic geometries. This condition is useful in situations where the ow rate is known, or more importantly, in cases where the pressure gradient is not known a priori, such as in countercurrent ows. Using the present condition, the ow rate is imposed at the inlet in terms of a bulk velocity, but the velocity ÿeld evolves as part of the solution. The condition is formulated to be suitable for both ÿxed and moving periodic domains. For the case of a moving domain, a correction is introduced to account for changes in the instantaneous velocity through the periodic edges. Under periodic conditions, these corrections integrate to zero over a complete (temporal) period. The new periodic condition is shown to produce accurate results for at and wavy-walled channels under both induced ow and countercurrent conditions.

On the interplay between inertial and viscoelastic effects for the flow in weakly modulated channels

“…For Newtonian uid ow inside modulated channels, Zhou et al [13,14] compared the ÿrst-order perturbation results to simulations obtained using ÿnite volume approach [44]. The validity of the ÿnite-volume code itself was established by comparison with the experimental results of Nishamura et al [33,34].…”

“…By taking advantage of the mapping approach, one also adopts the essence of the perturbation method to reduce the complicated transformed governing equations into a set of ordinary di erential equations subject to simple boundary conditions. For Newtonian uid ow inside modulated channels, Zhou et al [13,14] compared the ÿrst-order perturbation results to simulations obtained using ÿnite volume approach [44]. The validity of the ÿnite-volume code itself was established by comparison with the experimental results of Nishamura et al [33,34].…”

A volume‐based discrete test filter for conducting large eddy simulations with application to physiological flow in a constricted tube

“…The duct considered is D × D in cross-section and 6.4D long, and was initially discretized in the same manner as by Ham et al [27], using 48 uniform divisions along the duct length and 64×64 non-uniform, but orthogonal divisions in the cross-section, resulting in a non-uniform, orthogonal hexahedral grid. Wall conditions were imposed on the four sides of the duct, while the inlet and outlet were assumed to be periodic with one another and treated using the mass-based periodic condition developed by El Soukkary and Straatman [28]. Use of this periodic condition as opposed to the more conventional pressure-based condition enables the direct imposition of the Reynolds number and proved to provide converged solutions in 10-20% less CPU time than the pressure-based condition.…”