On the Port-Hamiltonian Structure of the Navier-Stokes Equations for Reactive Flows

We consider the problem of nding an energy-based formulation of the Navier-Stokes equations for reactive ows. These equations occur in various applications, e. g., in combustion engines or chemical reactors. After modeling, discretization, and model reduction, important system properties as the energy conservation are usually lost which may lead to unphysical simulation results. In this paper we introduce a port-Hamiltonian formulation of the one-dimensional Navier-Stokes equations for reactive ows. The port-Hamiltonian structure is directly associated with an energy balance, which ensures that a temporal change of the total energy is only due to energy ows through the boundary.

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