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Preprint 25-2015

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

Source file is available as :   Portable Document Format (PDF)

Author(s) : Robert Altmann , Philipp Schulze

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 25-2015

MSC 2000

37K05 Hamiltonian structures, symmetries, variational principles, conservation laws
76V05 Reaction effects in flows

Abstract :
We consider the problem of finding an energy-based formulation of the Navier-Stokes equations for reactive flows. 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 flows. 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 flows through the boundary.

Keywords : Reactive Flow, Port-Hamiltonian Formulation, Navier-Stokes Equations, Hamiltonian Formulation, Energy-Based Modeling

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