Numerical Calculation of Two-Phase Flows

The theoretical study of time-varying two-phase flow problems in several space dimensions introduces such a complicated set of coupled nonlinear partial differential equations that numerical solution procedures for a high-speed computer are required in almost all but the simplest examples. Efficient attainment of realistic solutions for practical problems requires a finite difference formulation that is simultaneously implicit in the treatment of mass convection, equations-of-state, and the momentum coupling between phases. We describe such a method, discuss the equations on which it is based, and illustrate its properties by means of examples. In particular, we emphasize the capability for calculating physical instabilities and other time-varying dynamics, at the same time avoiding numerical instability. The computer code is applicable to problems in reactor safety analysis, the dynamics of fluidized dust beds, raindrops or aerosol transport, and a variety of similar circumstances, including the effects of phase transitions and the release of latent heat or chemical energy.