2019_Numerische Methoden in der Umweltphysik

Diese Vorlesung vermittelt Grundlagen welche zur Entwicklung und Anwendung numerischer Modelle im Umweltbereich notwendig sind. Dazu gehört eine Einführung in die mathematische Modellierung gewöhnlicher und partieller Differentialgleichungen, sowie Uebungen zur Entwicklung und Programmierung einfacher Modelle.

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Kapitel 1: Einleitung und Überblick | protected page Skript | Slides: protected page Einleitung

Kapitel 2: Klassifikation numerischer Probleme | protected page Skript | Slides: protected page Advection

Kapitel 3: Methode der Finiten Differenzen | protected page Skript | Slides: protected page Finite Differences | protected page Numerical Order | protected page CFL-Criterion | protected page Waves | protected page von Neumann |  protected page Convergence

Kapitel 4: Zeitschrittverfahren | protected page Skript | Slides: protected page Klassifikation | protected page Implizite Advektion | protected page Runge Kutta

Kapitel 5: Nichtlineare Instabilitaet | protected page Skript | Slides: protected page Nichtlinearitaet

Kapitel 6: Konservative Verfahren | protected page Skript | Slides: protected page Konservative Verfahren

Kapitel 7: Beispiele aus der Umweltphysik | protected page Skript  

Kapitel 8: Ausblick | protected page Skript | Slides: protected page Ausblick

Kapitel 9: Literatur | protected page Skript  

This page is intended for students that require this course towards admission to an MSc program, but do not understand German. We deal with this situation as follows:

• We do not expect that you attend the lectures, but you need to attend the tutorials (all handouts and documentation is available in English, introduction to Python can also be taught in English).

• We supply some reading material in English that roughly covers the contents of the course.

• In fulfillment of the course, we will arrange for an oral examination (about 30 minutes). The date is halfway flexible (late December – early February, depending upon availability). Please contact me early in December to arrange a date.

Recommended reading material

(A) protected page Schaer2011_Ch2_Numerics.pdf: This is an overview of the material covered. I use the file as a repetition of finite difference methods in the course "numerical modeling of weather and climate". The file roughly covers what you will need from the current course in the master Atmospheric and Climate Sciences (but does not contain any explanations and derivations).

(B) protected page Riddaway2001_NumMethods.pdf: these are lecture notes. They extend far beyond the current course and you do not need to study the whole document, but merely chapters 1-3. In addition, you can omit most of section 1.4 (for the exam I will restrict attention to finite difference methods), subsections (i) and (iii) of section 2.5(a), and subsection 2.

(C) protected page Durran1998_Extract.pdf: This is an extract from Dale Durran’s book. From the pages provided, you can drop section 2.2.1 and section 2.3.3

With this selection, some of our course's content is not covered (most importantly, the Runge Kutta schemes), while other parts may be covered in a bit more depth and with a bit more rigor. However, we are happy to restrict the material to what is mentioned above. Note also that the material provided in (B) and (C) partly overlaps with each other. Regarding document (B), it might be easier to start with section 2 rather than section 1.