This course will cover principles and practice for modelling complex physical systems, including how to choose the appropriate physical laws, apply simplifying assumptions that make the problem tractable, as well as choices around the most suitable computational approach for solving the model. We will model multi-physics systems from micro to macro scales using homogenisation approaches. Two computational methods, used extensively in research and industry, will be examined: the traditional Finite Element Method (FEM) and Smooth Particle Hydrodynamics (SPH), a modern meshless method used for solving non-linear problems in both fluid and solid mechanics. This part of the course will cover the underlying theories, computational techniques, industry applications, and the use of commercial software.
The course is divided into 3 modules, each of 4 weeks duration. The first module will cover theory and application of the finite element method to multi-physics problems; the second module will cover theory and application of multi-scale and homogenisation approaches to analysing physical systems in solid mechanics problems; and the third module will cover theory and application of smoothed particle hydrodynamics to fluid and wave problems.