Skip to main content

Applied and Computational Mathematics Research Group

Our research in applied and computational mathematics includes: theoretical and applied fluid mechanics, mathematics and mechanics of solids, mathematical biology, applied analysis, and numerical analysis and scientific computing.

Our research in the area of applied and computational mathematics is informed by problems at the interface with physical sciences, biological sciences and engineering and there are many productive interdisciplinary collaborations within Cardiff University and further afield. Interdisciplinary collaborators at Cardiff University include colleagues in Biosciences, Earth and Environmental Sciences, and Engineering.

Our national and international collaborators include research groups at Barcelona, Oxford, Cambridge, MIT, Manchester, Edinburgh, Cyprus, Duke, Mexico City

Our research has applications in the early detection of tsunamis, deep water transportation, granular flows such as debris avalanches, subsea landslides and pharmaceutical powder processing, biomechanics, materials science, process engineering, calcium signalling in fertilization and embryogenesis, magnetic targeting for bio applications and other biofluids challenges, morphogenesis, cellular motion, Stochastic dynamics, neurobiology, oncology.

The group hosts the Cardiff University Student Chapter of the Society for Industrial and Applied Mathematics and the Institute of Mathematics and its Applications (SIAM-IMA Student Chapter) which encompasses postgraduate students and faculty members from across the University who are interested in mathematics or scientific computing and their real-world applications.


The main areas of research within the current group are:

Theoretical and applied fluid mechanics

Free-surface flows, dynamics of liquid films and jets, hydrodynamic stability theory, laminar-turbulent transition mechanisms, boundary-layer and wake flow instabilities, acoustic-gravity waves, viscoelastic flows, bubble dynamics, constitutive modelling of polymeric liquids, granular flow, geophysical flow modelling, non-Brownian suspensions.

Mathematics and mechanics of solids

Nonlinear elasticity, nonlinear viscoelasticity, contact problems, limit states analysis, constitutive modelling in materials science, strain-limiting theory of material response.

Mathematical biology

The development of mathematical, computational and statistical methods to address biological and medical problems.

Applied analysis

Inverse problems in materials modelling, homogenisation and the mechanics of composites. Calculus of variations.

Numerical analysis and scientific computing

The development and analysis of algorithms for the numerical solution of partial differential applications.

We are keen to supervise students in these areas. To give a more specific flavour of our work to date, recent examples of PhD topics supervised by our group include:

  • Stochastic finite strain analysis of inhomogeneous hyperelastic solids
  • Underwater earthquake characterization by acoustic radiation analysis
  • Stochastic modelling and analysis of homogeneous hyperelastic solids
  • Debonding and stretching of biogenic cellular structures
  • Linear stability and transient behaviour of viscoelastic fluids in boundary layers
  • Efficient spectral element methods for partial differential equations
  • Droplet dynamics on heterogeneous surfaces
  • Theoretical and computational modelling of compressible and non-isothermal viscoelastic fluids.

Meet the team

No picture for Ahlam Alghamdi

Ahlam Alghamdi

Research student

Picture of Arthur Davies

Professor Arthur Davies

Honorary Distinguished Professor

+44 29208 75522
Picture of Usama Kadri

Dr Usama Kadri

Reader in Applied Mathematics

+44 29208 75863
Picture of Katerina Kaouri

Dr Katerina Kaouri

Reader (Associate Professor)

+44 29208 75259
Picture of Angela Mihai

Professor Angela Mihai

Professor of Applied Mathematics, Director of Research

Picture of Timothy Phillips

Professor Timothy Phillips

Chair in Applied Mathematics

+44 29208 74194
Picture of John Pryce

Professor John Pryce

Emeritus Professor

Picture of Layla Sadeghi Namaghi

Miss Layla Sadeghi Namaghi

Research student

Picture of Yasemin Sengul Tezel

Dr Yasemin Sengul Tezel

Lecturer in Applied Mathematics

+44 29208 75554
Picture of Yidan Xue

Dr Yidan Xue

Post Doctoral Research Associate


Next steps


Research that matters

Our research makes a difference to people’s lives as we work across disciplines to tackle major challenges facing society, the economy and our environment.


Postgraduate research

Our research degrees give the opportunity to investigate a specific topic in depth among field-leading researchers.


Our research impact

Our research case studies highlight some of the areas where we deliver positive research impact.