The hybrid Cartesian grid/gridless method for simulating viscous flows

The hybrid Cartesian grid/gridless method is developed to simulate viscous flows. The flow field is basically discretized by Cartesian grids, and local gridless treatment is embedded in the region adjacent to the body. In order to simulate the thin boundary layer of the viscous flows interested in this paper, the cloud of anisotropic points is implemented in the local gridless region. A cloud overlap-free procedure is proposed which enables the hybrid method to treat complex flows involving close-coupled bodies. The unstructured Cartesian grid needed for the hybrid method is generated based on the quadtree data structure, which can help to control the quality of the clouds at the interface between the grid region and the gridless region. The resulting hybrid method is applied to solve two-dimensional compressible NS equations. The viscous flows past a NACA0012 airfoil and a RAE2822 airfoil are first simulated, and the numerical results obtained present a good agreement with available experimental data. The paper ends with a numerical example of the viscous flow past a two-element airfoil, which demonstrates the ability of the present method for treating more complex flows over multi-bodies.