The ability to refine quadrilaterals will allow me to process grids which discretize boundary layer regions with quadrilaterals and use triangles elsewhere. This is an important step to being able to handle more realistic configurations which utilize quads/triangles in 2-D and prisms/tetrahedrons in 3-D. Since * Cobalt* uses unstructured grids, I allow quadrilaterals to be refined as a mix of triangles and quadrilaterals. This allows the refinement to remain localized.

My first test case contains only quadrilaterals in the grid. It is the axi-symmetric bump of Bachalo and Johnson. The slideshow below presents the grid in the top image and the corresponding solution, colored by pressure, in the bottom image. A pressure difference of 5% was used as the refinement criteria.

The grid statistics are provided in the table below. The grid score has not suffered as much as the pure triangle grids had.

Original | Refinement 1 | Refinement 2 | Refinement 3 | Refinement 4 | |
---|---|---|---|---|---|

Number of Points | 22,321 | 23,268 | 24,496 | 25,672 | 28,087 |

Number of Faces | 44,320 | 46,439 | 49,310 | 51,972 | 57,517 |

Number of Cells | 22,000 | 23,172 | 24,815 | 26,301 | 29,431 |

Grid Score | 96.19 | 96.13 | 96.03 | 95.98 | 95.87 |

The second case is a NACA0012 which resolves the boundary layer with quads and uses triangles outside the BL. This case was run at a transonic condition to generate a shock along the airfoil for shock/BL interaction. The original and refined grids plus solution, colored by Mach number, are shown below. A pressure difference of 5% was also used to determine refinement for this case.

The table below shows the grid statistics for the original and refined NACA0012. The grid score has gone down by 1.21 over the four refinements.

Original | Refinement 1 | Refinement 2 | Refinement 3 | Refinement 4 | |
---|---|---|---|---|---|

Number of Points | 22,041 | 23,227 | 25,483 | 27,566 | 31,349 |

Number of Faces | 56,167 | 59,183 | 64,972 | 71,143 | 82,492 |

Number of Cells | 34,126 | 35,956 | 39,489 | 43,577 | 51,143 |

Grid Score | 98.48 | 98.33 | 98.05 | 97.71 | 97.27 |