An approximation of source terms in gradient form for multiphase transport processes

A set of two model equations for a multiphase flow is chosen to investigate the influence of approximation formulas. The approximations have been applied to the prediction of Peclet numbers using control volume interface values, as well as for gradient terms occurring as source terms. Use of an exponential approximation for a gradient source term, instead of the conventional central-difference approximation, leads to a remarkable reduction in the number of control volumes required. Different approximation formulas for the predictions of the grid Peclet number are found to have little influence on results. The form of the model equation has also been investigated. The source terms in gradient form in the model have been combined with the convection and diffusion terms to become part of the discretization scheme.