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Nerovnovážná termodynamika hyperbolických systémů
Thesis title in Czech: Nerovnovážná termodynamika hyperbolických systémů
Thesis title in English: Non-equilibrium thermodynamics of hyperbolic systems
Key words: Nerovnovážná termodynamika, hyperbolicita, nespojitá Galerkinova metoda, mechanika kontinua
English key words: Non-equilibrium thermodynamics, hyperbolicity, discontinuous Galerkin method, continuum mechanics
Academic year of topic announcement: 2018/2019
Type of assignment: dissertation
Thesis language:
Department: Mathematical Institute of Charles University (32-MUUK)
Supervisor: RNDr. Michal Pavelka, Ph.D.
Author:
Advisors: RNDr. Jaroslav Hron, Ph.D.
prof. RNDr. Vít Dolejší, Ph.D., DSc.
Dr. Marco La Mantia, Ph.D.
Guidelines
1) Survey of Hamiltonian mechanics in continuum physics [1]
2) Review of Symmetric hyperbolic thermodynamically compatible (SHTC) equations including their Hamiltonian and dissipative nature, e.g. within the GENERIC framework [1,2,3]
3) Extension of SHTC to mixtures and hyperbolic self-propelling heat conduction (e.g. superfluids [4])
4) Numerical solution of the thermodynamic equations (e.g. by discontinuous Galerkin ADER WENO [5,6])
References
[1] Michal Pavelka, Václav Klika and Miroslav Grmela. Multiscale Thermo-Dynamics, de Gruyter (Berlin), 2018
[2] Ilya Peshkov, Michal Pavelka, Evgeniy Romenski, Miroslav Grmela, Continuum Mechanics and Thermodynamics in the Hamilton and the Godunov-type Formulations, Continuum Mechaanics and Thermodynamics 30(6), 1343-1378, 2018.
[3] Hans Christian Öttinger, Beyond Equilibrium Thermodynamics, Wiley 2005
[4] Mongiovì, Maria Stella; Jou, David; Sciacca, Michele, Non-equilibrium thermodynamics, heat transport and thermal waves in laminar and turbulent superfluid helium, Physics Reports, Volume 726, p. 1-71, 2018
[5] Haran Jackson, A fast numerical scheme for the Godunov–Peshkov–Romenski model of continuum mechanics, Journal of Computational Physics, Volume 348, Pages 514-533, 2017
[6] Michael Dumbser, Francesco Fambri, Maurizio Tavelli, Michael Bader and Tobias Weinzierl, Efficient Implementation of ADER Discontinuous
Galerkin Schemes for a Scalable Hyperbolic PDE Engine, Axioms 2018, 7, 63;
Preliminary scope of work in English
Some questions that might be addressed by this work:
1) How does fully hyperbolic formulation of fluid mechanics correspond to the solutions to Navier-Stokes-Fourier equations?
2) How are dislocations mechanically propagated within the fluid?
3) And is there actually any difference between fluids and solids (except for different energy and dissipation potential)?
4) How to treat several self-propelling momenta present within the continuum?
5) Can the one-component models of superfluid Helium be formulated as Hamiltonian systems with algebraic dissipation?
6) How to prescribe interface interaction between fluids and solids properly within the hyperbolic framework?
 
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