  We present a lattice method for determining scattering phase shifts and
mixing angles for the case of an arbitrary number of coupled channels. Previous
nuclear lattice effective field theory simulations were restricted to mixing of
up to two partial waves for scattering of two spin-$1/2$ particles, which is
insufficient for analyzing nucleon-nucleus or nucleus-nucleus scattering
processes. In the proposed method, the phase shifts and mixing angles are
extracted from the radial wave functions obtained by projecting the
three-dimensional lattice Hamiltonian onto the partial wave basis. We use a
spherical wall potential as a boundary condition along with a channel-mixing
auxiliary potential to construct the full-rank $S$ matrix. Our method can be
applied to particles with any spin, but we focus here on scattering of two
spin-$1$ bosons involving up to four coupled channels. For a considered test
potential, the phase shifts and mixing angles extracted on the lattice are
shown to agree with the ones calculated by solving the Schr\"odinger equation
in the continuum.
