Port-Hamiltonian formulation of two-phase flow models

Two-phase flows are frequently modelled and simulated using the Two-Fluid Model (TFM) and the Drift Flux Model (DFM). This paper proposes Stokes–Dirac structures with respect to which port-Hamiltonian representations for such two-phase flow models can be obtained. We introduce a non-quadratic candidate Hamiltonian function and present dissipative Hamiltonian representations for both models. We then use the structure of the corresponding formally skew-adjoint operator to derive a Stokes–Dirac structure for the two variants of multi-phase flow models. Moreover, we discuss the difficulties in deriving a port-Hamiltonian formulation of the DFM with general slip conditions, and argue why this model may not be energy-consistent.