\begin{document}$ v_{1} $\end{document}) of light hadrons produced in Au+Au, Ru+Ru, and Zr+Zr collisions at \begin{document}$\sqrt{s_{NN}}=$\end{document} 200 GeV. The evolution of tilted energy density, pressure gradient, and radial flow along the x-direction is systematically investigated. The counter-clockwise tilt of the initial fireball is shown to be a vital source of directed flow for final light hadrons. A good description of directed flow is provided for light hadrons in central and mid-central Au+Au and isobar collisions at the RHIC. Our numerical results show a clear system size dependence for light hadron \begin{document}$ v_{1} $\end{document} across different collision systems. We further study the effect of nuclear structure on the directed flow and find that \begin{document}$ v_{1} $\end{document} for light hadrons is insensitive to nuclei with quadrupole deformation."> Hydrodynamic simulations of directed flow for light hadrons in Au+Au and isobar collisions at <inline-formula><tex-math id="M1">\begin{document}${ \sqrt{{\boldsymbol s}_{\boldsymbol{NN}}}=}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/800ce746-c66d-4d6b-b1cf-5d188384b428/CPC-2022-0371_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/800ce746-c66d-4d6b-b1cf-5d188384b428/CPC-2022-0371_M1.png"/></alternatives></inline-formula> 200 GeV -
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