Special aspects of numerical mathematics

Wintersemester 2024/25

Vorlesung

 
Dozent

Prof. Dr. Christian Rohde

Assistenz
Zeit und Ort

Vorlesung mit Übung:

Do 08:00 – 11:15,
PWR57-7.122

 

 

 
Inhalt

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

Theoretische und praktische Lösungsstrategien für stochastische Probleme aus verschiedenen naturwissenschaftlichen Bereichen.

Vorkenntnisse

Grundlagen in Numerischen Methoden für PDEs und in Wahrscheinlichkeitsrechnung

Literatur
  • Wird in der Vorlesung bekannt gegeben.
Curricula

M.Sc. Mathematik, LA Mathematik, M.Sc. SimTech

Leistungspunkte

9

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