Numerische Methoden in der Umweltphysik
We plan to hold all lectures and tutorials in the class room CHN E46.
Streaming and Recordings: The lecture and tutorials will be only held in the class room. There will be no streaming or recordings of the lectures.
Piazza: We offer the possiblity to ask questions concerning the content of the lectures and the tutorial through external page Piazza.
Language: The lectures and lecture notes will be in German. The tutorial will be held in English.
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.
Outline: Download Administratives (PDF, 391 KB)
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 | protected page Higher Order
Kapitel 4: Zeitschrittverfahren | protected page Skript | Slides: protected page Classification | protected page Implicit Advection | 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 | siehe auch Tutorial
Kapitel 8: Ausblick | protected page Skript | protected page Slides Teil 1 | protected page Slides Teil 2
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.
