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Modeling the transport of deformable capsules under different flow regimensis crucial in a variety of fields, including oil rheology, blood flow and thedispersion of pollutants. The aim of this study is twofold. Firstly, a combinedLattice Boltzmann-Immersed Boundary (LBM-IB) approach is developed forpredicting the transport of inertial deformable capsules. A Moving LeastSquares (MLS) scheme has been implemented to correlate the pressure, velocityand force fields of the fluid domain with the capsule dynamics. Thiscomputational strategy has been named LBM Dynamic IB. Secondly, this strategyis directly compared with a more conventional approach, named LBM Kinematic IB,where capsules move with the same velocity of the surrounding fluid. Multipletest cases have been considered for assessing the accuracy and efficiency ofthe Dynamic over Kinematic IB scheme, including the stretching of circularcapsules in shear flow, the transport in a plane Poiseuille flow of circularand biconcave capsules, with and without inertia. By monitoring the capsulegeometry over time, the two schemes have been documented to be in excellentagreement, especially for low Capillary numbers (Ca $\leq$ 0.01), in the caseof non-inertial capsules. Despite a moderate increase in computational burden,the presented LBM Dynamic IB scheme is the sole capable of predicting thedynamics of both non-inertial and inertial deformable capsules. The proposedapproach can be efficiently employed for studying the transport of blood cells,cancer cells and nano/micro capsules within a capillary flow.

Kinematic and dynamic forcing strategies for predicting the transport of inertial capsules via a combined lattice Boltzmann-Immersed Boundary method