Efficiency, thermodynamic calculation example

Likewise, efficient interface reconstruction algorithms and mixed cell thermodynamics routines have been developed to make three-dimensional Eulerian calculations much more affordable. In general, however, computer speed and memory limitations still prevent the analyst from doing routine three-dimensional calculations with the resolution required to be assured of numerically converged solutions. As an example. Fig. 9.29 shows the setup for a test involving the oblique impact of a copper ball on a hardened steel target... 

Comparison of numerical efficiencies of computing either directly or on the basis of thermodynamic integration leads us to the discussion of an important trick for these calculations stratification. We focus here on a specific example, but the general advantage of stratification can be considered in a much less specific context statistical uncertainties are mitigated by a nonstatistical subdivision of the problem, solution of the subdivided problems, and then recomposition of the whole (Hammersley and Handscomb, 1964, Section 5.3 Kalos and Whitlock, 1986, Section 4.5 Press etal, 1992, Section 7.8). 

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