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Course material I created for the tutorial "Mathematical Modelling in Climate Research" at the Freie Universität Berlin

License: Apache License 2.0

Jupyter Notebook 99.66% Python 0.34%
burgers-equation heat-equation python scientific-computing shallow-water-equations tutorial-course finite-difference-method finite-volume-method

mmidk's Introduction

Mathematische Modellierung in der Klimaforschung

This repository contains the course material I created as a voluntary lecturer for the tutorial Mathematical Modelling in Climate Research at the Freie Universität Berlin. The .tex files used to generate the lecture notes are available upon request.

Course outline

week content exercise Python crash course
w0 an introduction to Git
w1 introduction to numerics with a simple harmonic oscillator Using scipy.integrate.odeint [solution] functions and lists
w2 discretising the simple harmonic oscillator; numerical stability discretising and solving the Lotka-Volterra equations [solution] for loops and list comprehension
w3 order of accuracy and convergence; error analysis
w4 discretising and solving the heat equation implement an FTCS scheme [solution] good programming practices
w5 [review of knowledge acquired]
w6 conservation laws
w7 Burger's equation; finite volume method, Lax-Friedrich, and the CFL condition discretising and solving the Burgers' equation [solution]
w8 error analysis of the Lax-Friedrich method
w9 using a debugger and profiler modularising the exercise from w7 classes
w10 shallow water equations; Richtmyer-Lax-Wendroff method [final proj.] implement the discretised shallow water equations
w11 dealing with boundary conditions and source terms [final proj.] implement the discretised shallow water equations
w12-15 implement and run the shallow water code; describe the simulation results [final proj.] implement the discretised shallow water equations

License

The material provided in this repository may be freely used, modified, and distributed, subject to an attribution to this repository.

References

The material from week ten onwards was adapted from Paul Connolly's webpage on the Shallow Water Equations.

The two textbooks I used extensively in preparing these material were Randall J. LeVeque's

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