Shockwave-bubble test cases

Shown in Table 8 are the mesh sizes for the three-dimensional shock-bubble interaction test cases. The number of mesh vertices were 262K, 568K, and 1.03M. This test case computes the interaction of a shockwave moving through a low density fluid and interacting with a bubble of high density fluid. The explicit three-stage time scheme of Shu and Osher [#!shu!#] was used to advance the solution in time.

Table 8: Shockwave-bubble test Cases

Test cases	No. vertices	Code
3d Shock-bubble interaction	262K	AEDIF
3d Shock-bubble interaction	568K	AEDIF
3d Shock-bubble interaction	1.03M	AEDIF

**Figure 4:** Test case: Shockwave-bubble symmetry plane density profile
$\begin{figure}\centerline{\psfig{figure=bubble000symmetry_plane.eps,width=0.8\textwidth}} \centering\end{figure}$

Figure 4 and Figure 5 show the initial symmetry plane density contours (10:1 density ratio) and the three-dimensional density contours after 720 time steps at which time the shockwave has passed through the bubble reflected off the top boundary and passed through the bubble a second time.

**Figure 5:** Shockwave-bubble density contours after 720 time steps
$\begin{figure}\centerline{\psfig{figure=bubb3d_Rho.720crop1.eps,width=0.8\textwidth}} \centering\end{figure}$

Table 9: 262K mesh: Comparison of Globus performances on individual clusters

Run type	Globus	Globus	Globus	Globus
Name of cluster	INRIA-nina	IUSTI	INRIA-pf	CEMEF
Processor speed	2 GHz	2 GHz	1 GHz	1 GHz
LAN speed	1.00 Gbps	100 Mbps	100 Mbps	100 Mbps
cache	512K	512K	256K	256K
RAM/Node	1 GB	1 GB	1/2 GB	1/2 GB
Executable size	871 MB	871 MB	871 MB	871 MB
Number of processors	8	8	8	8
Total computational time	331.4	341.2	564.7	759.6
Local inter-comm. time	2.0	7.2	9.1	12.6
Global inter-comm. time	8.6	9.5	16.6	35.3
Computation ratio	1.00	1.03	1.7	2.3
Communication/Work	0.03	0.05	0.05	0.07