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FLASH Code Test Results
2-D Bow Shock with Mach 3 Wind
The two dimensional bow shock is a useful test of hydrodynamic codes since it is a supersonic problem that is particularly sensitive to the errors introduced by gridding schemes. Quirk (1994) discusses the 2-D bowshock as well as some of the problems that arise and recommends a solution. The simulations presented here were performed with the FLASH 2.4 code and do implement Quirk's recommendation (namely to use a Riemann HLLE solver on the site of the shock to increase dissipation). This fix is included in the FLASH 2.4 distribution.
The problem uses a two dimensional rectangular domain which is 3 units wide and 1.8 units high. A reflecting step 0.2 units wide is centered in the domain facing the left-to-right supersonic wind. The other details of the setup (i.e. wind, density, and boundary conditions) are identical to that of the windtunnel with a step problem.
The bow shock problem was studied quantitatively with FLASH 2.4 in a section of Orban and Ricker (2004) with the goal of verifying the accuracy of the vorticity generation behind the shock. Comparisons of other variables to analytic results were also performed in Orban (2005). The full text of that study is availible here.
The visualizations and images shown here are from the results of Orban (2005) at 3 levels of adaptive mesh refinement (AMR). This gives an effective grid of 480x288 zones.
| Density |
| Pressure with AMR block structure |
| Vorticity |
| 3-level run | Density, Pressure and Vorticity for t=0.5 (JPG) | |
| Density, Pressure and Vorticity for t=1.0 (JPG) | ||
| Density, Pressure and Vorticity for t=1.5 (JPG) | ||
| Density, Pressure and Vorticity for t=2.0 (JPG) |
References
Orban, C.M., 2005, "Modelling Protogalactic Collapse and Magnetic Field Evolution with FLASH." Undergraduate senior thesis, University of Illinois at Urbana-Champaign.
Orban, C.M. and P.M. Ricker, "Modelling Protogalactic Collapse and Magnetic Field Evolution with FLASH." 2004, BAAS, 36, 1499.
Quirk, J.J., "A Contribution to the Great Riemann Debate", Int. J. Numer. Methods Fluids 18, 555 (1994).
