A survey of numerical methods for shock physics applications Page: 12 of 22
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discontinuity and the shock are slightly smeared by the diffusion in the advection scheme and the
artificial viscosity, respectively. Both of these effects are substantially reduced in the higher reso-
lution simulation.
Figure 5 displays a comparison of CTH and SPH (SPHINX) results for the similar initial condi-
tions (larger pressure and density gradients were used to further stress each code). CTH used 1000
zones to span the space and SPHINX used 1000 equal smoothing length interpolation points. The
SPHINX setup did not include mass matching across the discontinuity which could have im-
proved the results. The smoothing length is generally considered to be a rough measure of the res-
olution of an SPH code. ALEGRA was also run against the same initial conditions in both
Figure 5: CTH and SPHINX Solutions for the Sod Problem
S10.1
101 T0I"
0 2 4 6 8 10v
101
X (CM) 6.0 6.4 6.8 7.2 7.6 8.0
X (m)
Eulerian and Lagrangian mode. The ALEGRA/Eulerian results were nearly identical to those of
CTH and the ALEGRA/Lagrangian results were intermediate in accuracy to those of CTH and
SPHINX. Similar simulations have been done with the finite difference Lagrangian code WON-
DY. This code has algorithms specifically designed for shock matching and past experience has
shown extremely accurate representations of features similar to those in Figure 4. The slight verti-
cal offset between the CTH results and SPHINX results is due to differences in the way each code
parameterizes the equations of state, not to underlying errors in either method. The overshoot seen
in the SPH results is disturbing and has been noted by other authors, particularly Benson (1992).
Mass matching of the interface particles and other special remedies may reduce this phenomena.
Explosively Formed Projectile
As a second example I consider a more complex problem, The simulation of Explosively Formed
Projectiles (EFP) is of general interest because of the range of dynamics covered in such
calculations. High explosive detonation, material strength and failure, and thermodynamic
extremes (hot and cold materials in contact) make this class of simulations especially useful for
testing purposes. The computational representation of the EFP is shown in Figure 6. The EFP
consisted of a 360 gm OFHC copper liner and approximately 1000 gm of LX-14 high explosive
encased in a 1600 gm AISI 4340 steel case. The initial inner diameter of the EFP was
approximately 11.7 cm, and the center-line distance between the inner surface of the steel case and
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Hertel, E. S., Jr. A survey of numerical methods for shock physics applications, article, October 1, 1997; Albuquerque, New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc697116/m1/12/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.