A Variational Framework for Reactive Flows and Shock Waves

Abstract eng:
For physical systems formulated within the framework of Lagrange formalism the dynamics is completely defined by only one function: the Lagrangian. This concept successfully applies e.g. to Newtonian mechanics, quantum mechanics, electrodynamics and nuclear physics. In continuum theories, however, many open problems remain up to date. In this paper is shown how reactive flows and shock waves are embedded into the framework of Lagrange formalism: motivated by ideas formulated by Anthony [1], an existing Lagrangian of Seliger and Whitham [2] for adiabatic baroclinic flow is extended towards flows with chemically reacting agents along the line of a systematic procedure [3]. A key feature is the use of complex fields, invoking discontinuities of the Lagrangian for irreversible processes and therefore requiring an extension of the general formalism. This allows for elaborating systems in thermofluiddynamics with discontinuities in general and with shock waves in particular. The present state of the theory and examples are shown.

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