  We report on the first evidence for a non-zero rapidity-odd directed flow
($v_{1}$) for $D^{0}$ and $\overline{D^{0}}$ mesons in 10-80\% centrality Au+Au
collisions at $\sqrt{s_{\rm NN}}$ = 200~GeV measured with the STAR detector at
RHIC. The slope of the $v_1$ rapidity dependence ($dv_{1}/dy$) averaged over
$D^{0}$ and $\overline{D^{0}}$ mesons is -0.081 $\pm$ 0.021 $\pm$ 0.017, while
that of charged kaons is -0.0030 $\pm$ 0.0001 $\pm$ 0.0002, suggesting
significantly larger slope for the $D^{0}$ mesons. Models indicate that the
large $dv_{1}/dy$ of $D^{0}$ mesons is sensitive to the initially tilted
source. We also present a new measurement of the $D^{0}$ meson elliptic flow
($v_2$) as a function of transverse momentum ($p_{T}$) in Au+Au collisions at
$\sqrt{s_{\rm NN}}$ = 200~GeV with an improved precision with respect to the
previously published results.The $D^{0}$ $v_{2}$ results are compared to those
of light-flavor hadrons to test the number-of-constituent-quark (NCQ) scaling.
Both the $v_{1}$ and $v_{2}$ results are compared to recent hydrodynamic and
transport model calculations.
