At this scale of description, fluid flow is described by continuum equations, such as the Navier-Stokes equation. There are applications to both pure science and engineering, aided by the development of new algorithms and new mathematical theory.
Continuum fluid dynamics
Fluid flow is an active area of research in mathematics, science and engineering with a wide range of applications. Research concerns the study of novel physical systems, new mathematical and algorithmic developments and applications to aeronautical, chemical and mechanical engineering.
In the Department of Mathematics, research is no just into liquids and gases. Many flowing materials, such as slurries and multiphase mixtures, display 'fluid like' behaviour and can be tackled using techniques developed for classical fluid problems. Much of the emphasis in our work is placed on the nonlinear behaviour in these 'fluid like' systems. More information can be found on the Department of Mathematics website:
Computational fluid dynamics research covers a range of activities related to the modelling and simulation of complex and challenging fluid flow problems in aerospace, power generation, nuclear, environmental, reservoir modelling and chemical processing (computational fluid dynamics CFD; modelling and simulation; Department of Chemical Engineering and Analytical Science research themes). Novel numerical techniques and treatments are also developed and tested to allow the most efficient solution of complex problems using a range of methods.
Smooth Particle Hydrodynamics
Smooth Particle Hydrodynamics (DSPH) is one of the most exciting new areas in the field of computational fluid and solid dynamics and has been a major research activity in MACE for over 10 years through the leadership of Dr Benedict Rogers, Prof Peter Stansby and Dr Steve Lind.
This meshless method is opening up the possibility of research into fields that were well beyond any modelling capability but are now being actively pursued, from violent free-surface flows to viscoelastic flows in containers to hardware acceleration using graphics processing units (GPUs).
More information is given on:
Solid Mechanics research is an area of vital importance in many branches of engineering, geophysics, and material science. The subject continues to develop at a rapid rate as new materials and designs are introduced to meet the stringent demands of industry; the latter requirements may include the need for lightness, strength, heat resistance etc. Theoretical study by applied mathematicians is essential to advance the understanding of the fundamental mechanical and dynamical properties of such materials, to provide new mathematical tools and insights into the field, and of course to estimate the potential for fracture or other catastrophic failure in situ. Such theoretical work also offers novel approaches to anticipating the behaviour of ever-more-complex materials being employed by material scientists, especially in the field of nanotechnology and metamaterials.
Groups working in this general area include:
We also note the research done on waves. In the Department of Mathematics waves are studied in heterogeneous media, of which good examples are composite materials and bone. The complex microstructure of such materials gives rise to a complex wave field. Often the interest is how an effective wave propagates through the medium. In order to study problems in this domain, many different types of mathematics are required including the development of fundamental analytical techniques, computational methods, probability theory and the use of many aspects of the theories of acoustics, elasticity and water waves. For more information, visit:
The Modelling and Simulation Centre (MaSC)
MaSC is a University of Manchester Research Centre that makes use of continuum modelling to investigate topics ranging from the micro-structure of materials to the flow of ocean currents. It forms part of the Dalton Nuclear Institute and has strong links with the Materials Performance Centre, The University of Manchester Aerospace Research Institute (UMARI), the Tyndall Centre and the Laser Processing Centre.
Among its specialisms are: