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- Configuration for the spherical case:

- Euler equations in two- and three-dimensions, using an ideal gas (air with )
- Van-Leer flux vector splitting with Godunov dimensional splitting

- AMR-computation with coarse grid of 40x40x32; up to four additional refinement levels, each with refinement factor 2
- approximately 1400 timesteps with CFL-No. 0.8 to t=3 (approx. 1200 timesteps to t=2.5 for computation with 4 additional refinement levels)
- computational domain 1.25x1.25x1; sphere radii 0.16 and 0.08 respectively
- Timing information ...

- Force coefficients on second body as a function of axial displacement for simulations with 3 additional refinement levels:

- Drag coefficient on first sphere:

- Color plot of pressure distribution in 3D:

Additional levels | ||||

1 | 1.264 | -0.176 | ||

2 | 1.442 | 0.178 | -0.019 | 0.157 |

3 | 1.423 | -0.019 | 0.052 | 0.071 |

4 | 1.408 | -0.015 | 0.087 | 0.035 |

As may be seen, in this configuration the force coefficients (lift expecially) are quite sensitive to changes in the refinement level. This is due to the improved shock resolution for higher refinement levels, as may be seen in the following schlieren image, which shows the position of the shock for different additional refinement levels (2=blue, 3=red, 4=black). This improved resolution leads to a noticeable change in the impingement point of the shock on the secondary body.

This configuration thus represents a 'worst case' scenario - convergence is significantly improved if the secondary body is entirely inside the primary shock. For the computation with 3 additional refinement levels we estimate the error in the drag and lift coefficients to be 2% and 5% respectively of the drag coefficient value. The error in the experimental measurements is expected to be of the order of 5%.

-- StuartLaurence - 23 Jan 2005

I | Attachment | Size | Date | Who | Comment |
---|---|---|---|---|---|

spheres_drag.mpg | 1021.5 K | 02 Feb 2005 - 06:02 | StuartLaurence | Movie of flow startup with force histories on the two spheres | |

stable_schlieren.mpg | 4937.7 K | 04 Mar 2005 - 17:29 | StuartLaurence | Schlieren movie of stable flow over two cylinders | |

schlieren_3d.mpg | 808.4 K | 04 Mar 2005 - 21:51 | StuartLaurence | Computational schlieren movie of startup process over two spheres | |

unstable_schlieren.mpg | 8743.3 K | 10 Mar 2005 - 00:29 | StuartLaurence | Schlieren movie of unstable flow over two cylinders | |

stability_comparison.mpg | 16295.4 K | 10 Mar 2005 - 01:25 | StuartLaurence | Movie of schlieren superimposed on refinement level sets showing stable and unstable flow development |

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