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Lecturer(s)
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Course content
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Basic eqations of fluid dynamics: description of the flow, transport theorem, continuity equation, equations of motion, stress tensor, Euler and Navier-Stokes equations, energy equation, thermodynamical relations. Mathematical theory of compressible flow: Euler equations, properties of the Euler equations, Cauchy problem, boundary conditions, weak solution. Finite volume method: Finite volume mesh, derivation of the finite volume scheme, properties of the numerical flux, construction of the numerical flux, Godunov method, Riemann solver.
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Learning activities and teaching methods
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unspecified
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Learning outcomes
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Introduction to the mathematical modelling. The emphasis is put on the active learning of basic mathematical and physical concepts. Formulation of conservation laws in the form of the differential equations, constitutive and rheological relations, Euler equations, finite volume method, Riemann solver, numerical flux, adaptive methods, higher order methods.
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Prerequisites
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unspecified
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Assessment methods and criteria
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unspecified
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Recommended literature
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Feistauer M., Felcman J., Straškraba I. Mathematical and Computational Methods for Compressible Flow, Oxford University Press, Oxford. 2003.
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Feistauer M. Mathematical Methods in Fluid Dynamics. Longman Scientific-Technical, Harlow, l993.
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