Time-Constant Variation in the Collision-Breakup Equation

Abstract

Discretization of the collision-breakup equation results in a nonlinear system that can produce highly damped solution components. An analytic expression is derived for the smallest time constant τmin, a parameter used to describe the most rapid decay rate associated with the system. τmin is found to be a measure of the decay time for destruction of the largest drops considered in the model. For Marshall-Palmer distributions N0e?AD, τmin decreases with increasing N0 and with increasing rainfall rate R. τmin determines the maximum time step that can be used to insure computational stability in numerical solution of the breakup equation. For large N0 and R, time steps as small as 1 s may be required to prevent error growth.