Structure-Preserving Spatial Discretization of a Two-Fluid Model

We present a structure-preserving spatial discretization method for infinite-dimensional non-linear port-Hamiltonian representations of a commonly used one-dimensional two-phase flow model: the Two-Fluid Model. We introduce the port-Hamiltonian representation of this two-phase flow model and then invoke a mixed-finite-element method to perform a structure-preserving spatial discretization. Consequently, we obtain a finite-dimensional realization of a recently proposed novel Stokes-Dirac structure for this model. The properties of the resulting finite-dimensional realization are assessed and the conditions under which it is known to respect the properties of a finite-dimensional Dirac structure are discussed. Moreover, we derive the complete finite-dimensional interconnected port-Hamiltonian model by invoking the notion of power-preserving interconnection.