A general multi-component method for the description of dust grain processing.

We derive a special differential form of a balance or conservation equation for the grain size distribution function. This equation describes the evolution of the grain size spectrum in one-dimensional stationary flows also taking into account possible size dependent drift velocities of the grains relative to the gas flow. Various physical and chemical processes acting differently on grains of different size and velocities can be treated simultaneously: grain condensation, growth and evaporation, mechanical and chemical sputtering, grain coagulation and shattering. A corresponding computational multi-component method is presented and we provide some details on efficient implementation. As a test calculation the numerical scheme is applied to investigate mechanical sputtering of grains due to dense shocks.