An estimate of the rate of increase in numerical simulation grid sizes with time is obtained by counting the grids (measured in terms of number of node points) reported in the nine volumes of an established proceedings on the numerical modeling of solidification phenomena dating back to 1980. It is shown that the largest grids used in a given year increase at a rate consistent with the well-known Moore's law on computing power, i.e., the number of nodes in the grids double every 18 months. From this observation, approximate bounds on the available grid size in a current year are established. This approximation is used to provide projections as to when, assuming Moore's law continues to hold, direct simulations of physical phenomena, which resolve to the smallest scale present, will be achievable.
Bibliographical noteFunding Information:
This work was supported in part by the Minnesota Supercomputing Institute. FP-A was supported by the National Science Foundation through Grant EAR-0094200 and by NASA through Grant NAG5-10569. The authors appreciate the useful comments from Jon Dantzig, University of Illinois, and Christoph Beckermann, University of Iowa, on earlier drafts. The authors also thank the reviewers for insightful comments. In particular, the reviewer who suggested the inclusion of a single fit line for the data in Table I and the discussion on possible reasons why the Moore’s Law scaling should hold.