We present initial results for the application of a relativistic heavy-quark action in the charm sector on 2+1-flavor lattice ensembles produced by the CLS consortium. The five parameter action was tuned non-perturbatively using a neural network and continuum charmonium ground-state masses. We investigate masses of $D$-meson correlators produced on CLS ensembles X451 and N451 with pion masses of approximately $287$ MeV, as well as their dispersion relation. The meson correlators were produced using the stochastic distillation scheme. Additionally, we present expected energy levels of the $D\pi$-channel in meson-meson scattering up to the $\eta$-threshold and describe our setup for an ongoing determination of scattering amplitudes in the $D\pi$-scattering system.