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We present a hybrid spectral element-Fourier spectral method for solving thecoupled system of Navier-Stokes and Cahn-Hilliard equations to simulatewall-bounded two-phase flows in a three-dimensional domain which is homogeneousin at least one direction. Fourier spectral expansions are employed along thehomogeneous direction and $C^0$ high-order spectral element expansions areemployed in the other directions. A critical component of the method is astrategy we developed in a previous work for dealing with the variabledensity/viscosity of the two-phase mixture, which makes the efficient use ofFourier expansions in the current work possible for two-phase flows withdifferent densities and viscosities for the two fluids. The attractive featureof the presented method lies in that the two-phase computations in thethree-dimensional space are transformed into a set of de-coupledtwo-dimensional computations in the planes of the non-homogeneous directions.The overall scheme consists of solving a set of de-coupled two-dimensionalequations for the flow and phase-field variables in these planes. The linearalgebraic systems for these two-dimensional equations have constant coefficientmatrices that need to be computed only once and can be pre-computed. We presentample numerical simulations for different cases to demonstrate the accuracy andcapability of the presented method in simulating the class of two-phaseproblems involving solid walls and moving contact lines.

A Three-Dimensional Hybrid Spectral Element-Fourier Spectral Method for Wall-Bounded Two-Phase Flows