  We present an effective method for simulating wall-bounded multiphase flows
consisting of $N$ ($N\geqslant 2$) immiscible incompressible fluids with
different densities, viscosities and pairwise surface tensions. The N-phase
physical formulation is based on a modified thermodynamically consistent phase
field model that is more general than in a previous work, and it is developed
by considering the reduction consistency if some of the fluid components were
absent from the system. We propose an N-phase contact-angle boundary condition
that is reduction consistent between $N$ phases and $M$ phases ($2\leqslant
M\leqslant N-1$). We also present a numerical algorithm for solving the N-phase
governing equations together with the contact-angle boundary conditions
developed herein. Extensive numerical experiments are presented for several
flow problems involving multiple fluid components and solid-wall boundaries to
investigate the wettability effects with multiple types of contact angles. In
particular, we compare simulation results with the de Gennes theory for the
contact-angle effects on the liquid drop spreading on wall surfaces, and
demonstrate that our method produces physically accurate results.
