Direct quadrature method of moment on characteristic volume for population balance equation

Direct quadrature method of moment with nominal volume of entities for a general population balance model (PBE) is proposed. In order to lower time consumption in the simulation, the entity intrinsic property is extracted from the numerical density function of entity distribution by Gauss quadrature approximation and moment transformation. The higher accuracy and the lower time consumption are validated in aggregation, breakage and growth cases in isotropic system. The number or volume of the entities is self-conservative due to their automatic tracking in the simulation. With volume as internal coordinates, volume moment can be tracked, too. As a result, it is preferable for describing precipitation in crystal system. This method enables to solve mass transfer of incompressible multi-fluid systems with chemical reactions according to the proportional relationship between the mass of the disperse phase and its volume.