Lecturer: Dr Stephen Millmore
The underlying theory behind the simulation of continuum matter is a mix of mathematics, physics and numerical analysis. It is expected that students have a good understanding of aspects of these topics, but there may be some areas which were not covered in previous courses, or, at least, not in sufficient detail. Within this course, the necessary background in all these areas will be covered, such that all students have sufficient background for the examinable continuum-stream courses. The topics covered by this course are:
- Vector calculus
- Multivariable calculus (with some thermodynamics)
- Partial differential equations and integral equations
- Measuring the error in discretisation
- Iterative solution techniques, including solution of ordinary differential equations
In addition to revising these areas, they will all be set in the framework of solving the equations of continuum modelling, motivating some of the work that is to come in later courses.
Lectures:
1) Vector calculus
2) Multivariable calculus and partial differential equations
3) Discretisation and error
4) Root finding and iterative ordinary differential equation solvers
Prerequisites:
None
Required course for:
- Numerical Methods for Compressible Fluid Dynamics
- Numerical Methods for Incompressible Fluid Dynamics
Picture credit: Stephen Millmore