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Numerical Modelling I & II: Theory & applications
Last Updated: 2026-02-05 15:24:10
Abstract
In this integrated 13-week sequence (Numerical Modeling I and II), students will learn how to write programs from scratch to solve partial differential equations that are useful for Earth science applications. Programming will be done in MATLAB and will use the finite-difference method. The course will emphasise a hands-on learning approach rather than extensive theory.
Objective
The goal of this course is for students to learn how to program numerical applications from scratch. By the end of the course, students should be able to write MATLAB programs that solve systems of partial-differential equations relevant to Earth Science applications using the finite-difference method. Applications include wave propagation, diffusion, advection, low Prandtl-number rotating convection, solid mechanics and convection, groundwater flow, and multiple-body gravitational interactions. The emphasis will be on commonality, i.e., using a similar approach to solve different applications, and modularity, i.e., re-use of code in different programs by writing it as functions. The course will emphasise a hands-on learning approach rather than extensive theory, and will begin with an introduction to programming in MATLAB.
Content
A provisional week-by-week schedule (subject to change) is as follows: ---------Numerical Methods I-------- Week 1: Introduction to programming in Matlab Week 2: Introduction to the finite difference approximation to differential equations. Week 3: Integrating ordinary differential equations (e.g., time-evolution problems). Application: multiple-body gravitational interactions. Week 4: Programming the div(K.grad(scalar)) term. Application: scalar wave propagation. Week 5: Solving the time-dependent diffusion equation. Week 6: Solving the Poisson equation using a direct (matrix) solver. Application: potential fields. Week 7: Poisson equation with variable coefficients. Application: diffusion with implicit time-dependence. ---------Numerical Methods II-------- Week 8: Advection in 1-D and 2-D. Comparison of different methods and their accuracy. Week 9: Combining advection and flow calculation I. Application: Groundwater flow using Darcy’s law. Week 10: Combining advection and flow calculation II: Convection at low Prandtl number. Week 11: Solving Stokes flow (i.e., infinite Prandtl-number) using primitive variables. Week 12: Advanced topics, e.g., variable-viscosity Stokes flow, tracer advection, multigrid solvers. Week 13: Review GRADING will be based on weekly homeworks (mostly involving programming) and a term project to develop an application of their choice to a more advanced level.
General Information
- Language
- English
- Levels
- MSC
- Frequency
- Yearly recurring
Examination
- Type
- end-of-semester examination
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture with exercise |
Numerical modeling I: theory
Courses Numerical modelling I and II have to be taken together and will be examined together at the end of the semester
|
|
4 h weekly |
| lecture with exercise |
Numerical modeling II: applications
Courses Numerical modelling I and II have to be taken together and will be examined together at the end of the semester
|
|
4 h weekly |