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Lecturer(s)
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Jelínek Petr, doc. RNDr. Ph.D.
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Belov Sofya, Mgr.
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Course content
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1. Introduction - limits of theoretical and experimental methods, numerical simulations as a bridge between theory and experiment, models and reality, description of physical problems, difference between particle and fluid approach 2. Mathematical description of the continuum, classification of partial differential equations and their use in physics - elliptic, parabolic and hyperbolic equations 3. Hydrodynamics, application (propagation of sound waves) 4. Discretization methods and numerical solutions - finite difference method, finite volume method, initial and boundary conditions 5. Numerical solutions of elliptic and parabolic PDEs, implicit, explicit methods, Crank-Nicholson scheme 6. Numerical experiments - parabolic equations (transport equation, heat conduction equation, Burgers equation) 7. Numerical experiments - elliptic equations (Laplace and Poisson equations) 8. Numerical experiments - instabilities (Rayleigh-Taylor, Kelvin-Helmholtz, Richtmyer-Meshkov) 9. Description of plasma - continuous description, magnetohydrodynamics (MHD) 10. MHD equation in conservative form 11. Numerical solutions of hyperbolic equations 12. AMR - adaptive mesh refinement, flux limiters 13. MHD waves, waves in inhomogeneous media 14. Numerical experiments - hyperbolic equations (Friedrichs diagrams, MHD wave propagation)
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Learning activities and teaching methods
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Monologic (reading, lecture, briefing)
- Class attendance
- 30 hours per semester
- Semestral paper
- 10 hours per semester
- Preparation for exam
- 20 hours per semester
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Learning outcomes
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The aim of the course is to acquaint students with approaches of numerical solutions of problems in the continuum (astrophysical plasma) using fluid modelling. The main task will be to solve problems especially in astrophysical plasmas, using approximations from two-fluid models, through single-fluid models to magnetohydrodynamics. Emphasis will be placed on the ability of practical use of individual algorithms and approaches.
The student will be able to solve physical and mathematical problems by methods of fluid and magnetohydrodynamic numerical simulations.
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Prerequisites
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Basic courses in general and theoretical physics, mathematics and numerical methods.
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Assessment methods and criteria
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Oral examination, Seminar work
Answer at least 70% of the questions in the test.
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Recommended literature
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Chung, T. J. Computational fluid dynamics. New York : Cambridge University Press, 2006. ISBN 0-521-59416-2.
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Kulhánek, P.:. Úvod do teorie plazmatu. Praha: AGA, 2011. ISBN 978-80-904582-2-2..
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Murawski, Krzysztof. Analytical and numerical methods for wave propagation in fluid media. Singapore : World Scientific, 2002. ISBN 981-238-155-4.
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Priest, Eric Ronald. Magnetohydrodynamics of the Sun. First published. New York : Cambridge University Press, 2014. ISBN 978-0-521-85471-9.
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Tajima, Toshiki. Computational plasma physics : with applications to fusion and astrophysics. Boulder : Westview Press, 2004. ISBN 0-8133-4211-2.
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