Unsteady Acceleration of Multiple Spheres

In this simulation, 57 spheres are accelerated by a uniform hypersonic freestream of Mach number 10. The spheres are orignally in a face-centered-cubic configuration of a roughly spherical shape. This configuration is held until a steady flow has been established, at which point the spheres are given an impulsive acceleration away from their common center. The subsequent motion is determined by the aerodynamic loadings experienced, but over the timeframe of the simulation the induced velocities are small compared to the initial velocities. The slices show density profiles on various planes, while the contour is one of density gradient, and shows the position of the bow shockwave. [source codes]

The details of the computation are as follows:

• Euler equations in three dimensions, ideal gas (air with %$\gamma=1.4$%)
• Van-Leer flux vector splitting with Godunov dimensional splitting
• AMR-computation with coarse grid of 48x48x48; two additional refinement levels, refinement factors 2,2
• 1078 timesteps with CFL-No. 0.4 (to t=0.4) and 0.7 to t=1.5
• computational domain 1.6x1.6x1.6; all sphere radii 0.08
• density ratio = 1430 (sphere material density/freestream gas density)
• approximately 4800 hrs CPU time on 48 and 192 CPUs

• spheres.mpg: Movie of moving spheres

• Initial configuration of the spheres:
  

-- StuartLaurence - 20 Aug 2005