A Hybrid Cartesian-Body Fitted Grid Approach for Simulation of Flows in Complex Geometries

A novel approach of automated hybrid Cartesian-body ¯tted grid (HCBFG) for simulations of °uid °ows in complex geometries is suggested. Based on a Cartesian background grid, the new approach automatically searches a near wall boundary(NWB) at any instant when a geometry is given. Within the NWB, a body-¯tted mesh is generated using an e±cient algebraic method with the skew angle between any two mesh lines guaranteed between 45 ± and 135±. This is attributed to the fact that only the mesh lines tangential to the solid surface needs to be generated. The mesh lines in the other two directions are from the background Cartesian grid. Outside of the NWB, the Cartesian grid is used. On the NWB, the grid points are one-to-one connected with the Cartesian grid. Hence, a consistent discretization scheme for structured grid can be used with no interpolation needed at the NWB. The fully conservative °ux calculation can be achieved. This new approach has the advantages of the Chimera grid and Cartesian grid methods to treat complex or moving geometry, but overcomes the drawbacks of those methods requiring inter-polation on the di®erent mesh boundaries. Bene¯ted from the HCBFG, all the rigorous numerical techniques developed for body-¯tted grid, which are essential to achieve high order accuracy, can be used. The mesh size of the proposed hybrid grid approach will also be substantially smaller than that of a Cartesian grid method or unstructured grids since a highly stretched grid can be used near walls. This new approach may open a door to a new class of CFD technique for e±ciently and accurately simulating steady and unsteady °ows, furthermore, solving moving grid and °uid-structural interaction problems with complex geometries. This paper presents several examples of the HCBFG for representative geometries. The transonic RAE2822 airfoil is calcu-lated using an implicit line Gauss-Seidel iteration to demonstrate the feasibility of the method.