Coupling of lattice Boltzmann (LB) and phase-field (PF) methods is discussed for simulation of a range of multiphase flow problems. The local relaxation and shifting operators make the LB method an attractive candidate for the simulation of the single-phase as well as multiphase flows. For simulating interface dynamics, LB methods require to be coupled with an appropriate scheme representing interfacial dynamics. To this end, we have used a model based on the order parameter, which could be either an index function or a phase-field variable, and coupled it with a LB solver for the simulation of various classes of complex multi-physics and multiphase flows. The LB method is used to compute the flow-field, and, in the case of electrodeposition process modeling, the electro-static potential-field. The application of such a coupled LB-PF is illustrated by the solution of a variety of examples. Finally, fast simulation of such a coupled algorithm is achieved using the state-of-art numerical solution acceleration techniques involving preconditioning and multigrid approaches.

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