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Main Title: Operator-GENERIC Formulation of Thermodynamics of Irreversible Processes
Author(s): Moses Badlyan, Arbi
Zimmer, Christoph
Type: Research Paper
Abstract: Metriplectic systems are state space formulations that have become well-known under the acronym GENERIC. In this work we present a GENERIC based state space formulation in an operator setting that encodes a weak-formulation of the field equations describing the dynamics of a homogeneous mixture of compressible heat-conducting Newtonian fluids consisting of reactive constituents. We discuss the mathematical model of the fluid mixture formulated in the framework of continuum thermodynamics. The fluid mixture is considered an open thermodynamic system that moves free of external body forces. As closure relations we use the linear constitutive equations of the phenomenological theory known as Thermodynamics of Irreversible Processes (TIP). The phenomenological coefficients of these linear constitutive equations satisfy the Onsager-Casimir reciprocal relations. We present the state space representation of the fluid mixture, formulated in the extended GENERIC framework for open systems, specified by a symmetric, mixture related dissipation bracket and a mixture related Poisson-bracket for which we prove the Jacobi-identity.
Subject(s): GENERIC
thermodynamics of irreversible processes
Onsager-Casimir reciprocal relations
operator equation
weak formulation
Issue Date: 14-Aug-2018
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 35Q35 Other equations arising in fluid mechanics
37K05 Hamiltonian structures, symmetries, variational principles, conservation laws
37L99 None of the above, but in this section
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2018, 07
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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