Energy-conserving formulation of the two-fluid model for incompressible two-phase flow in channels and pipes

We show that the one-dimensional (1D) two-fluid model (TFM) for stratified flow in channels and pipes (in its incompressible, isothermal form) satisfies an energy conservation equation, which arises naturally from mass momentum equations constitute model. This result extends upon earlier work on shallow water (SWE), with important difference we include non-conservative pressure terms analysis, propose a formulation holds ducts arbitrary cross-sectional shape, 2D channel circular pipe geometries as special cases. The second novel of this is finite volume scheme TFM discrete form continuous equation. discretization derived manner runs parallel to analysis. Due it essential employ staggered grid, requires careful consideration defining fluxes, relations between them Numerical simulations confirm conserved.