  We lay out the framework to numerically study nonlinear structure formation
in the context of scalar-field-coupled cold dark matter models (phiCDM models)
where the scalar field phi serves as dynamical dark energy. Adopting parameters
for the scalar field which yield a realistic CMB spectrum, we generate the
initial conditions for our Nbody simulations, which follow the spatial
distributions of 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 both the voids and clusters of
dark matter. The phiCDM model differs from standard LCDM at small scales with
observable modifications of, e.g., the mass function of halos as well as the
matter power spectrum. Nevertheless, the predictions of both models for the
Hubble expansion and the CMB spectrum are virtually indistinguishable. Hence,
galaxy cluster counts and weak lensing observations, which probe structure
formation at small scales, are needed to falsify this class of models.
