Synopsis

This practical numerical analysis course forms an essential part of the MSc and takes place every week in Hilary term. During term two topics are studied, each over four weeks. In the first and fifth week there is an introductory lecture on the topic and method needed to carry out the practical. In the following three weeks, students meet in groups for an hour class on their work which should be carried out before the class. Students submit a four or five page report for each of the two topics for assessment. All practical work can be done using matlab and techniques learned during the Michaelmas term practical course.

The first topic involves simulation of a test carried out on oil wells during drilling, called a drill stem test. The pressure around the well can be modelled by an unsteady diffusion equation and students develop a simulation by implementing a time marching, finite difference scheme.

The second topic involves simulation of a shock propagating along a tube. The simulation uses a technique called Roe's method to discretise the unsteady inviscid compressible one-dimensional Euler equations and so to track the transient propagation of a shock from a high to a low pressure region of gas. The practical requires students to implement the given discretisation scheme using matlab.

No prior knowledge of fluid mechanics is assumed or needed to carry out these exercises.