Artificial acceleration in accumulation due to coarse mass-coordinate divisions in numerical simulation

Abstract

The effects of coarse mass-coordinate divisions in numerical computations of the coagulation equation are examined. The numerical accuracy is essential to the estimate of the growth times of dust and planets. Three different logarithmic divisions with common ratios of √2, 2, and 8 are used to numerically solve the coagulation equation in cases of simple coalescence rates, where analytic solutions are known. The comparison of numerical solutions and analytic ones shows appreciable discrepancies between them and the discrepancies are quite large in the cases of larger common ratios; the coagulation is considerably accelerated. Comparison between the simulations of planetary growth with these three types of divisions is also made to show that growth time in early stages differs by a factor of about 10 between the cases of common ratios √2 and 8. This suggests that the previous numerical simulations of the coagulation process using coarse divisions with common ratios of 2 or 8 were very likely affected by this artificial acceleration.