A general framework for the thermodynamically consistent time integration of open nonlinear thermoelastic systems. Issue 1 (17th December 2018)

• Record Type: Journal Article
• Authors: Schiebl, Mark; Betsch, Peter
• Other Names: Müller G. guestEditor.; Ulbrich M. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 18:Issue 1(2018)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2018-12-17
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201800136
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: This work deals with Energy‐Momentum‐Entropy (EME) consistent methods of open thermoelastic systems. While Energy‐Momentum (EM) preserving integrators are well‐known for conservative mechanical systems, Romero introduced in [1] the class of thermodynamically consistent (TC) integrators for coupled thermomechanical systems, which further respect symmetries of the underlying coupled system and are capable of conserving associated momentum maps and can therefore also be termed EME schemes in analogy to EM schemes for conservative systems. As mathematical framework for the geometric structure of the non‐equilibrium thermodynamics the GENERIC (General Equation for Non‐Equilibrium Reversible‐Irreversible Coupling) framework, originally introduced for complex fluids in [2], is used. Since the GENERIC framework does not depend on a specific choice of the thermodynamical state variables [3], we explore the structure of the GENERIC framework using the entropy density (see e.g. [4]), the absolute temperature (see e.g. [5]) and further the internal energy density as thermodynamical state variable. Applying the notion of a discrete gradient in the sense of [6] leads to an EME integrator. As boundary conditions rely on the specific choice of the thermodynamical state variable we extend the GENERIC framework to be suitable for open systems following the procedure in [7].