A FLUX METHOD FOR THE NUMERICAL-SOLUTION OF THE STOCHASTIC COLLECTIONEQUATION

A new mass conservative flux method is presented for the numerical sol ution of the stochastic collection equation. The method consists of a two-step procedure. In the first step the mass distribution of drops w ith mass x' that have been newly formed in a collision process is enti rely added to grid box k of the numerical grid mesh with x(k) less tha n or equal to x' less than or equal to x(k+1). In the second step a ce rtain fraction of the water mass in grid box k is transported to k + 1 . This transport is done by means of an advection procedure. Different numerical test runs are presented in which the proposed method is com pared with the Berry-Reinhardt scheme. These tests show a very good ag reement between the two approaches. In various sensitivity studies it is demonstrated that the flux method remains numerically stable for di fferent choices of the grid mesh and the integration time step. Since a time step of 10 s may be used without significant loss of accuracy, the flux method is numerically very efficient in comparison to the Ber ry-Reinhardt scheme.