  Angular correlations of heavy-flavour and charged particles in high-energy
proton-proton collisions are sensitive to the production mechanisms of heavy
quarks and to their fragmentation as well as hadronisation processes. The
measurement of the azimuthal-correlation function of prompt D mesons with
charged particles in proton-proton collisions at a centre-of-mass energy of
$\sqrt{s} = 13$ TeV with the ALICE detector is reported, considering D$^{0}$,
D$^{+}$, and D$^{*+}$ mesons in the transverse-momentum interval $3 < p_{\rm T}
< 36$ GeV/$c$ at midrapidity ($|y| < 0.5$), and charged particles with $p_{\rm
T} > 0.3$ GeV/$c$ and pseudorapidity $|\eta| < 0.8$. This measurement has an
improved precision and provides an extended transverse-momentum coverage
compared to previous ALICE measurements at lower energies. The study is also
performed as a function of the charged-particle multiplicity, showing no
modifications of the correlation function with multiplicity within
uncertainties. The properties and the transverse-momentum evolution of the
near- and away-side correlation peaks are studied and compared with predictions
from various Monte Carlo event generators. Among those considered, PYTHIA8 and
POWHEG+PYTHIA8 provide the best description of the measured observables. The
obtained results can provide guidance on tuning the generators.
