High-Resolution Simulation of Multidimensional Crystal Growth

Many of the crystals in the pharmaceuticals, photographic, and other industries are multidimensional; that is, their growth is associated with the change of multiple internal coordinates. The main governing equation for such systems is a highly nonlinear multidimensional population balance equation that must be solved for a wide range of length scales. For population balance equations, it is well-known that the standard first-order schemes give diffusive solutions while the commonly used second-order schemes give spurious oscillations. This paper presents a high-resolution simulation algorithm that provides short computation times and high accuracy. The high-resolution algorithm is compared to the upwind difference and Lax−Wendroff methods through simulations of potassium dihydrogen phosphate (KDP, KH 2 PO 4 ) crystal nucleation and growth. No spurious oscillations or numerical diffusion occurred, in contrast to the upwind method and Lax−Wendroff methods. The numerical stability of the algorithm is assessed using the Courant−Friedrichs−Lewy condition.