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- Dozent
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Prof. Dr. Christian Rohde
- Assistenz
- Zeit und Ort
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Vorlesung mit Übung:
Do 08:00 – 11:15,
PWR57-7.122
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- Inhalt
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The lecture serves as an introduction to the modelling and numerics in fluid mechanics.
It starts with a derivation of the basic Euler and Navier-Stokes equations from first principles. We will discuss asymptotic regimes and equilibrium states that lead to the classical hierarchy of fluid dynamics: compressible and incompressible flow equations, the Stokes system.
The second part will be concerned with the analytical treatment of selected systems focussing on the Leray theory for the incompressible Navier-Stokes equations. Based on the analytical results we will introduce soem numerical approaches including Finite-Element approaches, Finite-Volume methods and articifical compressibility approaches. A special focus will be on asymptotic-preserving methods to handle extreme regimes like the Low-Mach number regime.
The lecture will conclude with the analytical treatment of homogenized models for flow in porous media uncluding the multiscale method.
- Lernziele
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Theoretische und praktische Lösungsstrategien für stochastische Probleme aus verschiedenen naturwissenschaftlichen Bereichen.
- Vorkenntnisse
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Grundlagen in Numerischen Methoden für PDEs und in Wahrscheinlichkeitsrechnung
- Literatur
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- Wird in der Vorlesung bekannt gegeben.
- Curricula
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M.Sc. Mathematik, LA Mathematik, M.Sc. SimTech
- Leistungspunkte
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9