  We lay out the frameworks to numerically study the structure formation in
both linear and nonlinear regimes in general dark-matter-coupled scalar field
models, and give an explicit example where the scalar field serves as a
dynamical dark energy. Adopting parameters of the scalar field which yield a
realistic CMB spectrum, we generate the initial conditions for our N-body
simulations, which follow the spatial distributions of the dark matter and the
scalar field by solving their equations of motion using the multilevel adaptive
grid technique. We show that the spatial configuration of the scalar field
tracks well the voids and clusters of dark matter. Indeed, the propagation of
scalar degree of freedom effectively acts a fifth force on dark matter
particles, whose range and magnitude are determined by the two model parameters
(mu, gamma), local dark matter density as well as the background value for the
scalar field. The model behaves like the LCDM paradigm on scales relevant to
the CMB spectrum, which are well beyond the probe of the local fifth force and
thus not significantly affected by the matter-scalar coupling. On scales
comparable or shorter than the range of the local fifth force, the fifth force
is perfectly parallel to gravity and their strengths have a fixed ratio
2gamma^2 determined by the matter-scalar coupling, provided that the chameleon
effect is weak; if on the other hand there is a strong chameleon effect (i.e.,
the scalar field almost resides at its effective potential minimum everywhere
in the space), the fifth force indeed has suppressed effects in high density
regions and shows no obvious correlation with gravity, which means that the
dark-matter-scalar-field coupling is not simply equivalent to a rescaling of
the gravitational constant or the mass of the dark matter particles.
