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Lecturer(s)
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Jelínek Petr, doc. RNDr. Ph.D.
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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 2. Mathematical description of the continuum, classification of partial differential equations and their usage in physics - elliptic, parabolic and hyperbolic equations 3. Conservation laws, conservation equations, Navier-Stokes equations, 1D Euler equation 4. Discretization methods and numerical solutions - finite difference method, finite volume method, initial and boundary conditions 5. Implicit, explicit methods, Crank-Nicholson schemes, Burgers equation 6. Numerical experiments - transport equations, heat conduction equations 7. Numerical experiments - wave equation, Poisson's equation 8. Linear waves - waves in homogeneous media, magnetohydrodynamic (MHD) waves, waves in inhomogeneous media 9. Numerical solutions of hyperbolic equations 10. Description of plasma - fluid description, MHD 11. MHD 12. Numerical solutions of magnetohydrodynamic - magnetohydrodynamic in conservative form 13. AMR - adaptive mesh refinement, flux limiters
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Learning activities and teaching methods
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Monologic (reading, lecture, briefing)
- Class attendance
- 30 hours per semester
- Preparation for exam
- 30 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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The basic courses of general physics, theoretical physics, mathematics and numerical methods.
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Assessment methods and criteria
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Oral examination
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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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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