The general periodic boundary condition for the lattice Boltzmann method has been modified to incorporate the pressure difference for fully developed periodic flows. The results demonstrated that, unlike other existing pressure boundary treatments, the proposed procedure/treatment does not generate nonphysical inlet and outlet flow disturbances while preserving the system periodicity. This method is readily applicable to a range of lattice Boltzmann simulations for systems with periodic electric potential and temperature fields.
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Zhang et al. (2006) studied this question.
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