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Sedov Explosion

The Sedov explosion problem (Sedov 1959) involves the self-similar evolution of a cylindrical or spherical blast wave from a delta-function initial pressure perturbation in an otherwise homogeneous medium. In practice, we initialize the code by depositing a quantity of energy E=1 into a small region of radius dr at the center of the grid. The pressure inside this volume, p'0, is given by

p0¢ = 3(g-1)E
(n+1)p drn
  ,
where n=2 for cylindrical geometry and n=3 for spherical geometry. We set g=1.4. (In running this problem we choose dr to be 3.5 times as large as the finest adaptive mesh resolution in order to minimize effects due to the Cartesian geometry of our grid.) Everywhere the density is set equal to r0=1, and everywhere but the center of the grid the pressure is set to a small value, p0=10-5. The fluid is initially at rest. In the self-similar blast wave which develops for t>0, the density, pressure, and radial velocity are all functions of x º r/R(t), where
R(t) = Cn (g) æ
ç
è 		Et2
r0
ö
÷
ø 		1/(n+2)  .
Here Cn is a dimensionless constant depending only on n and g; for g=1.4, C2 = C3 = 1 to within a few percent.

We have performed two sets of Sedov tests on Cartesian grids with FLASH 1.0. The first set of runs tested cylindrical symmetry (2D) using 2, 4, 6, and 8 levels of refinement, corresponding to effective grids with 162, 642, 2562, and 10242 zones, respectively. The second set of runs tested spherical symmetry (3D) using 4 and 5 levels of refinement, corresponding to effective grids with 643 and 1283 zones, respectively.

Plots
2D runs Comparison of angle-averaged profiles for different refinement levels at t=0.05 (GIF, Postscript)
Pressure colormap plus AMR block structure plot for the 8-level run at t=0.05 (GIF, Postscript)
3D runs Angle-averaged and RMS profiles for the 4-level run at t=0.05 (GIF, Postscript)
Angle-averaged and RMS profiles for the 5-level run at t=0.05 (GIF, Postscript)

References
Sedov, L. I. 1959, Similarity and Dimensional Methods in Mechanics (New York: Academic)

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This file was last modified on 10 October 1999.
The ASCI Flash Center is based at the University of Chicago under U. S. Department of Energy contract B341495. All material on these pages is Copyright © 1999 ASCI Flash Center.