Algorithms for coupled problems that preserve symmetries and the laws of thermodynamics: Part II: fractional step methods |
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| Authors: | Ignacio Romero |
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| Affiliation: | 2. Technical University of Munich, Department of Mechanical Engineering, Chair of Automatic Control, Boltzmannstraße 15, 85748 Garching, Germany;3. Univ. Grenoble Alpes, LCIS, 26902 Valence, France;1. Delft University of Technology, Faculty of Aerospace Engineering, Wind Energy Group, P.O. Box 5058, 2600 GB Delft, The Netherlands;2. Delft University of Technology, Faculty of Aerospace Engineering, Aerodynamics Group, P.O. Box 5058, 2600 GB Delft, The Netherlands;3. ICES, Institute for Computational Engineering and Sciences, 201 East 24th St, Austin, TX, USA;4. Shell Global Solutions, The Netherlands;1. European Commission, JRC, Institute for Energy and Transport, Westerduinweg 3, NL-1755 LE Petten, Netherlands;2. Imperial College London, SW7 2BX London, UK;1. Dipartimento di Ingegneria Informatica, Automatica e Gestionale ‘Antonio Ruberti’, Sapienza Università di Roma, via Ariosto 25, 00185 Roma, Italy;2. Laboratoire des Signaux et Systèmes, CNRS-Supelec, Plateau de Moulon, 91190 Gif-sur-Yvette, France;1. Institute of Geospheres Dynamics, Russian Academy of Sciences, Leninskii Prospekt 38-1, 119334 Moscow, Russia;2. German Aerospace Center, Institute of Planetary Research, Rutherfordstraße 2, D-12489 Berlin, Germany;3. Museum für Naturkunde, Invalidenstraße 43, D-10115 Berlin, Germany |
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| Abstract: | This article proposes a new type of discretizations for initial boundary value problems of thermodynamical systems. Based on a combination of finite elements in space and fractional step methods in time, we formulate algorithms that exactly preserve the symmetries and the laws of thermodynamics of the continuum problem. The algorithmic design is based on the GENERIC formalism of irreversible thermodynamics which naturally suggests the split of the evolution operator upon which our fractional step method is based. Although the emphasis of the article is on the generality of the results, as an illustration, a discretization of nonlinear, finite strain, thermoelasticity is presented. Numerical simulations are provided that verify the excellent performance of the new methods. |
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