| 86 | | === Run 5 - Mach Comparison (Mach 1.5, 10, 100) === |
| | 86 | These simulations were intended to explore the dependance of bow shock thickness (the distance between the edge of the bow shock and the clump surface) on the mach number of the impinging flow. For these runs, I moved the boundaries far enough away so that the bow shock did not reach them over the course of the simulation. The effective resolution of the clump was kept constant using AMR, but the resolution in the ambient medium was reduced to speed up the calculation. Given the ambient medium is uniform and stationary, reducing its resolution in this way is reasonable, so long as the shock front is resolved to the same effective resolution as in the fiducial case (which produced a well-converged solution as shown in earlier line plots of the front). |
| | 87 | |
| | 88 | |
| | 89 | The first set of plots shows a comparison of the bow shocks (for M=1.5, 10, 100) at the moment the forward shock wraps around the clump and converges on itself, thereby creating a ‘mach stem’ or stagnation point behind the clump. As these plots show, the bow shock thickness is roughly equal in the different cases. |
| | 96 | |
| | 97 | Some of the papers referenced in my library (see below) for shock/clump interactions present theoretical estimates for the thickness of the bow shock. The results presented here should be explored further to see if they align with these estimates. Further more, while the time scale on which the clump/bow shock boundary becomes unstable to the Kelvin-Helmholtz, Rayleigh-Taylor, and nonlinear thin shell instabilities is roughly a clump crushing time, I expect the wave length of the resulting instabilities may also be a function of the upstream mach number. |
| | 98 | |
| | 99 | Thus, varying the mach number of the upstream flow can answer two questions: |
| | 100 | |
| | 101 | 1. What is the dependance of bow shock ‘thickness’ (or, similarly the time scale to reach a steady state configuration) on the mach number of the upstream flow? |
| | 102 | |
| | 103 | 2. what is the relationship between upstream mach and the wave length of fluid instabilities excited along the shocked clump surface? |
| | 104 | |
| | 105 | |
| | 106 | === Run 5 - Mach Comparison (Mach 100 vs. 200 vs. 300) === |
| | 107 | |
| | 108 | Produced similar results as the previous set of mach runs. |
| 94 | | This set of runs is meant to see how to adequately track the shock front with AMR and the clump. As the resolution in the ambient medium goes down with AMR, we wish to provide adequate resolution around the shock front as to not degrade the solution. Am doing a quick test of an AMR simulation of the fiducial initial conditions with the resolution of the ambient medium decreased by a factor of 4, plus two levels of refinement on the clump and refinement triggered by density gradients. |
| | 112 | We want to track the shock front to the highest resolution possible to minimize numerical dissipation of the shock front as it traverses the grid.To achieve this, we need the AMR to refine the shock front to the max level possible. Additionally, we want the clump to be resolved adequately; as a rule of thumb the clump should have at least 64 zones per clump radius. |
| | 113 | |
| | 114 | To track the shock front, we could use refinement criterion based on density gradients as used here. As can be seen from these images, the shock front is refined to the maximum AMR level over the course of the simulation. The clump, however, is being refined to the max level just along its edge, which exhibits a sharp density gradient. Forcing the entire clump to be refined to the max level can be done upon initialization easily enough using a geometrical refinement object in the code. |
| | 115 | |
