A systematic approach to modeling coupled distributed dynamical systems by formulating them as partial differential equations and algebraic constraints (PDAEs) is presented. Several advantages of the PDAE formulation are listed and discussed. The challenges of ensuring well-posedness are also touched upon. The PDAE system is converted by semi-discretization into a corresponding DAE system. It is subsequently realized for the purpose of simulations using a recently emerging control based approach. Thus, the typical requirement of consistent initialization is avoided for a large class of systems. The PDAE formulation and the numerical solution approach are illustrated through a particular application: modeling of fluid-structure interactions in arterial hemodynamics.

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