Mooreʹs Law and Numerical Modeling

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 Mooreʹs 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 Mooreʹs law continues to hold, direct simulations of physical phenomena, which resolve to the smallest scale present, will be achievable.