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.
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