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This paper describes an automatic, complex geometries applicable, unstructured, curved two-dimensional mesh-generation method; it provides virtual boundary-layer-like near-body grids coupled with the smooth progression of offbody grids for viscous flow simulations. This method allows for the generation of near-body and offbody grids in one piece at the same phase to avoid mesh quality problems in transition areas. Different from most curved viscous mesh-generation approaches, this method is direct by using a simple vector-adding approach, which obviates a linear or nonlinear-elasticity analogy but still provides highly probable positive-Jacobian mesh elements. In addition, transformation from linear to curved meshes can be achieved by only deforming the necessary edges of the elements near domain boundaries while retaining the remaining noncurved edges to benefit the numerical simulation solvers. [ABSTRACT FROM AUTHOR]