A　localized　flexible　airfoil　at　low　Reynolds　numbers　is　modeled　and　the　aerodynamic　performance　is　analyzed　numerically.　With　characteristic　based　split　scheme,　a　fluid　solver　for　two　dimensional　incompressible　Navier-Stokes　equations　is　developed　under　the　ALE　framework,　coupled　with　the　theory　of　shallow　arch,　which　is　approximated　by　Galerkin　method.　Further,　the　interactions　between　the　unsteady　flow　and　the　shallow　arch　are　studied　in　detail.　In　particular,　the　effect　of　the　self-excited　vibration　of　the　structure　on　aerodynamic　performance　of　the　airfoil　is　investigated　deeply　at　various　angles　of　attack.　The　results　show　that　the　lift-to-drag　ratio　has　been　increased　greatly　compared　with　the　rigid　airfoil.　Finally,　the　relationship　between　the　self-excited　vibration　and　the　evolution　of　the　flow　is　analyzed　using　FFT　tools.