Nonet-Cartesian Grid Method for Shock Flow Computations

A nonet-Cartesian grid method, based on anisotropic/isotropic refinement, is presented for solving the Euler equations in gas dynamic problems. Grids are generated automatically, by the recursive subdivision of a single cell into nine subcells for isotropic nonet-Cartesian grids and into three subcells independently in each direction for anisotropic nonet-Cartesian grids, encompassing the entire flow domain. The grid generation method is applied here to steady inviscid shock flow computation. A finite difference formulation for the Euler equation using nonet-Cartesian grids is used to treat complex two-dimensional configuration. Results using this approach are shown to be competitive with other methods. Further, it is demonstrated that this method provides a simple and accurate procedure for solving flow problems involving multielement airfoils.