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We apply a quark combination model with equal-velocity combination (EVC)approximation to study the elliptic flow ($v_{2}$) of hadrons in heavy-ioncollisions in a wide collision energy range ($\sqrt{s_{NN}}=$ 27 - 5020 GeV).Utilizing the simple relationship between $v_{2}$ of hadrons and those ofquarks under EVC, we find that $v_{2}$ of up/down quarks obtained byexperimental data of proton is consistent with that obtained by data of$\Lambda$ and $\Xi$. $v_{2}$ of strange quarks obtained by data of $\Omega$ isconsistent with that obtained by data of $\Lambda$ and $\Xi$, and at RHICenergies it is also consistent with that obtained by data of $\phi$. This meansthat $v_{2}$ of these hadrons have a common quark-level source. Using data of$D^0$, we obtain $v_{2}$ of charm quarks with $p_T\lesssim 6$ GeV/c. We findthat under EVC charm quark dominates $v_{2}$ of $D$ mesons at low $p_{T}$ butlight-flavor quarks significantly contribute to $v_{2}$ of $D$ mesons in therange $3\lesssim p_{T}\lesssim8$ GeV/c. We predict $v_{2}$ of charmed baryons$\Lambda_{c}^{+}$ and $\Xi_{c}^{0}$ which show a significant enhancement atintermediate $p_{T}$ due to the double contribution of light-flavor quarks. Theproperties of the obtained quark $v_{2}$ under EVC are studied and a regularityfor $v_{2}$ of quarks as the function of $p_{T}/m$ is found.

Elliptic flow of hadrons in equal-velocity quark combination mechanism in relativistic heavy-ion collisions