On the Roles of Implicitness, Realizability, Boundary Conditions and Artificial Dissipation in Multidimensional Two-Fluid Simulations with Interfacial Forces

Abstract The authors’ recent research and experience related to several numerical aspects of multi-dimensional full-two-fluid modeling is summarized, with emphasis on formulation elements associated with the treatment of interfacial forces. Application interests in the areas of bubbly flow through ship propellers and in annular flows, both characterized by significant interface dynamics, have focused our development efforts on improving the accuracy and convergence characteristics of two-fluid Navier-Stokes codes which incorporate modeled terms for these forces. Four CFD formulation elements which address the presence of these momentum source terms are discussed including: 1) interfield and intervariable coupling (i.e. implicitness) of force model terms, 2) the formulation of interfacial force model sets that differentially and discretely satisfy realizability ( ), 3) the role of boundary conditions in obtaining stable, oscillation free solutions and 4) the formulation of artificial dissipation operators, with particular emphasis on cell-centered solution strategies. Staggered and cell-centered codes which solve the fully developed two-fluid system are used as demonstration platforms for several of the discretization strategies discussed. Results obtained with full-multi-fluid Navier-Stokes solvers are also used to demonstrate elements of the proposed methods.