Abstract: The geometric characteristics and external flow of the three-element airfoils problem are complex, and the high-quality mesh generation and numerical simulation are difficult, which is one of the challenging problems in the field of Computational Fluid Dynamics. In order to reduce the complexity of spatial mesh generation and realize the simulation of three-element airfoils viscous flow under the Cartesian mesh framework, an applicable overset Cartesian mesh generation method is established to reduce the complexity of spatial mesh generation. A Cartesian mesh adaptation technology with overset area scale matching is constructed to ensure smooth transition between different meshes. In the process of searching for the contribution cells of the overset area, a matching method is designed for different types of grids, and the data transfer method between the near-wall structured grid and the background Cartesian grid is constructed. On the basis of the above grid framework, the spatial and temporal discretization of the governing equations of viscous flow in different grid regions is carried out, and a matching numerical solver for viscous flow is constructed. Using the constructed numerical solver, a numerical example is used to verify the three-element airfoils problem in the state of high Reynolds number, the calculated results of the pressure coefficient of the whole wing and different booths are in good agreement with the experimental values, which proves the effectiveness and reliability of the proposed methodology.