A two-dimensional hybrid flaw solver has been developed for the accurate and efficient simulation of steady and unsteady flaw fields. The flaw solver was cast to accommodate two different topologies of computational meshes. Triangular meshes are adopted in the near-body region such that complex geometric configurations can be easily modeled, while adaptive Cartesian meshes are utilized in the off-body region to resolve the flow more accurately with less numerical dissipation by adopting a spatially high-order accurate scheme and solution-adaptive mesh refinement technique. A chimera mesh technique has been employed to link the two flow regimes adopting each mesh topology. Validations were made for the unsteady inviscid vortex convection and the unsteady turbulent flows over an NACA0012 airfoil, and the results were compared with experimental and other computational results.