John Tyndall Institute

Numerical methods provide the tools to approximate solutions to mathematical models that describe physical phenomena. These methods are essential for solving differential equations, which often arise in mechanics and other areas of science, engineering and mathematics. Key numerical methods include the finite element method (FEM), the boundary element method (BEM) and the finite difference method (FDM).

The finite element method (FEM) is a versatile numerical technique which is used to solve complex problems in structural mechanics, fluid dynamics, thermal analysis and electromagnetics. The FEM is significantly established over half a century and there are a number of standard computer packages to implement it. Finite element analysis relates to the application of a FEM package to a particular problem. We have significant experience in finite element analysis of structural problems.

CFD employs numerical methods, most importantly, the finite volume method (FVM) to solve and analyse fluid flow problems, usually modelled by the Navier-Stokes equations. As with the FEM, there are a number of established computer software packages that implement CFD and can simulate various fluid flow fields. We have used CFD to provide insights into fluid behaviour in various applications, such as the analysis of the interaction between blood flow and vascular structures in medical implants.

Computational acoustics is related to computational mechanics insofar as the sound field often resides in a fluid domain and the fluid pressure field forms the perceived sound. Acoustic fields often are the result of vibrating structures or interact with structures (fluid-structure interaction). We have expertise with the BEM in acoustics, with which only meshes of structural surfaces are required to simulate sound fields, with applications of loudspeaker simulation and engine noise.

Mathematics education is leveraging advanced tools and techniques to make learning more interactive and practical. In our institute, numerical methods, computational tools, and simulation visualisation are applied to mathematical models of engineering problems. The application of these techniques at the forefront of this educational evolution. It provides students with a deeper understanding and practical skills that prepare students for advanced studies and professional challenges in various fields.