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The subject of this course is the treatment of mathematical and numerical
methods and techniques used in dynamics of fluids and gases. The following
topics are included: the existence and uniqueness of the solution of the
incompressible Navier-Stokes equations, their numerical solution by the
finite element method, the basic theoretical results for the compressible
Euler equations and nonlinear hyperbolic systems of conservation laws and
their finite volume numerical approximations, the theory of approximate
Riemann solvers.
Last update: T_KNM (11.05.2004)
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To give the knowledge of mathematical methods applied in fluid dynamics Last update: T_KNM (16.05.2008)
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Feistauer M.: Mathematical Methods in Fluid Dynamics. Longman Scientific-Technical, Harlow, l993. Feistauer M., Felcman J., Straškraba I.: Mathematical and Computational Methods for Compressible Flow. Clarendon Press, Harlow, 2003. Last update: T_KNM (16.05.2008)
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Lectures in a lecture hall. Last update: T_KNM (16.05.2008)
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Examination according to the syllabus. Last update: T_KNM (16.05.2008)
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Brief overview of equations describing the flow, description of motion of fluids, the transport theorem, basic physical laws formulated in form of differential equations, constitutive and rheological relations, basic facts from the thermodynamics.
Inviscid compressible flow, the Euler equations describing the inviscid flow, nonlinear hyperbolic systems of first order, their basic properties, weak solutions, Riemann problem and its solution, the finite volume method for the numerical solution of the Euler equations and nonlinear hyperbolic systems. Last update: T_KNM (16.05.2008)
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basic knowledge of mathematical and functional analysis and numerical mathematics Last update: T_KNM (16.05.2008)
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