A quadtree-based adaptive Cartesian/Quad grid flow solver for Navier-Stokes equations.

*(English)*Zbl 0968.76053From the summary: We develop and demonstrate the quadtree-based adaptive Cartesian/Quad (quadrilateral) grid generator, grid adaptor and flow solver. Given the definition of geometries (cubic B-splines and straight line segments), geometrically-adaptive, body-fitted Quad grids are generated automatically. These grids are then overlapped with a large Cartesian cell which is subdivided recursively, until the Cartesian cells which are intersected by outer boundaries of the Quad grids have grid resolutions similar to the Quad cells. The final computational grid is then automatically produced through cell cutting. A Quadtree data structure has been used to store the grids. As a result, grid refinement and coarsening are trivial to accomplish. Finally, we develop a cell-centered second-order accurate viscous flow solver which supports arbitrary control volumes.

##### MSC:

76M12 | Finite volume methods applied to problems in fluid mechanics |

76N15 | Gas dynamics (general theory) |

##### Keywords:

grid adaptor; body-fitted Quad grids; Cartesian cells; Quadtree data structure; cell-centered second-order accurate viscous flow solver
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