A multi-domain direct boundary element formulation for particulate flow in microchannels
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In the present study, a multi-domain boundary element formulation is developed for high surface-area-to-volume ratio problems (i.e. particulate ﬂow in high as-pect ratio microﬂuidic channels, in a porous medium or in microﬂuidic devices with repetitive structures). The solution domain is decomposed into subdomains and the variable condensation technique is implemented. The solution matrices are built for each subdomain, and the matrices are updated at each time step only for the subdomains in which the particles move at each time step. Ghost domains, which are ﬁctitious domains encapsulating the interfaces between the subdomains, are also introduced in the formulation to treat the particles cross-ing the interfaces between the subdomains. The formulation reveals that the computation of the subdomain matrices is further simpliﬁed for solution domains composed of periodic structures. The results of our study revealed that speed-up values as high as 50 for 2D structures and 80 for 3D structures is achievable with the current formulation.