A network model for incompressible two-fluid flow and its numerical solution

In this paper we consider an incompressible version of the two-fluid network model proposed by Porsching (Nu. Methods Part. Diff. Eq., 1 , 295–313 [1985]). The system of equations governing the model is a mixed system of differential and algebraic equations (DAEs). These DAEs are then recast, through proper transformation, into a system of ordinary differential equations on a submanifold of ?ⁿ, for which uniqueness, existence, and stability theorems are proved. Numerical simulations are presented.