Article Dans Une Revue ESAIM: Proceedings and Surveys Année : 2025

A generic framework to derive systems of conservation laws with source terms and its application to heat conduction in fluid flows: an alternative to the method of moments in kinetic theory of gases?

Résumé

A generic framework to derive systems of conservation laws through the Stationary Action Principle is proposed. The equations are expressed in Eulerian coordinates while the variation of the action assumes an underlying Lagrangian description thus avoiding the need for any Lin constraint. The resulting models admit a supplementary conservation equation for the evolution of the Hamiltonian. We then use the newly developed framework to derive a hyperbolic model that includes heat conduction in the compressible fluid dynamics equations through the introduction of a new variable called the thermal impulse. The resulting model has already been obtained previously through the Stationary Action Principle but its derivation relied on several non-standard assumptions. Our new framework allows not only to lift these assumptions, but also to recover them as a consequence of the Stationary Action Principle. Finally, a comparison with a model including heat conduction derived through the kinetic theory of gases is conducted.

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hal-05091807 , version 1 (01-06-2025)
hal-05091807 , version 2 (11-06-2025)

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Ward Haegeman, Samuel Kokh, Marc Massot, Giuseppe Orlando. A generic framework to derive systems of conservation laws with source terms and its application to heat conduction in fluid flows: an alternative to the method of moments in kinetic theory of gases?. ESAIM: Proceedings and Surveys, 2025, 78, pp.80-97. ⟨10.1051/proc/202578080⟩. ⟨hal-05091807v2⟩
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