ray-chew / mmidk

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

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

• Numerical Methods for Conservation Laws
• Finite Volume Methods for Hyperbolic Problems