| 32 | |
| 33 | [[CollapsibleEnd]] |
| 34 | |
| 35 | [[CollapsibleStart(Foster and Chevalier (‘93))]] |
| 36 | |
| 37 | === Summary === |
| 38 | |
| 39 | Authors ran simulations with an outer density of 1/1000 the density at the outermost edge of the clump, whereas my simulations used 1/100. The ambient therefore had a large sound speed throughout the constant pressure medium (pressure = pressure in sphere at edge), and since the ambient region was very large, the pressure remained nearly constant throughout. They found that if the sphere was initialized with the Larson-Penston solution, it followed the analytical LP soln'. If grid was initialized to by the singular isothermal sphere, it followed Shu's solution. |
| 40 | |
| 41 | === Stability Tests === |
| 42 | |
| 43 | The 'marginally stable sphere' had a xi=xiCrit=6.451. A density enhancement of 1% above equilibrium value was needed to bring out expected stability behavior: |
| 44 | |
| 45 | * xi = 3, flow oscillated about v=0 for ~ 15 free fall times |
| 46 | * xi = 6.451, collapse happened in 5 ff times |
| 47 | * xi = 20, collapse happened in 6 ff times |
| 48 | |
| 49 | |