Computational Mathematics and Fluid Dynamics
Introductory para
Group members
| Academic | Research Interests |
|---|---|
| Prof Beth Wingate | |
| Prof Jan Sieber | Numerical methods applied to physical experiments, dynamical systems with delay |
| Prof John Thuburn | |
Themes
Click on the following tabs to learn more about the themes we are developing.
Numerical analysis
Numerical analysis proves in which sense numerical methods approximate the solutions of the equations underlying scientific software. This includes the questions such as
- Do errors decrease as one increases resolution and computational effort? If yes, at which rate?
- How well are conserved quantities from the equations (e.g., mass, energy, momentum,...) conserved in the numerical approximation for imperfect resolution?
- When and how fast do iterations converge for implicit solvers?
Group members' recent activities
- Prof. Beth Wingate: convergence of massively parallel-in-time methods for wave-propagation problems with oscillatory stiffness in geophysical fluid dynamics problems
- Prof. Jan Sieber: combination of feedback control with numerical methods in controllable physical experiments; numerical methods for problems with state-dependent or large delays
- Prof. John Thuburn: stability, convergence and preservation of conserved quantities for discretizations in current and next-generation dynamical cores for weather and climate modelling (current: ENDGame, next generation: GungHo)
Quasi-uniform meshes on the sphere avoid the polar singularities of the traditional longitude-latitude mesh, which leads to a severe communications bottleneck at high resolution on massively parallel machines in applications such as weather forecasting. We have been working with the Met Office to develop new numerical methods that exploit ideas from differential geometry to capture key conservation and balance properties and so remain accurate even on these exotic meshes.
Planetary and Environmental Science
A substantial research effort at the Departments of Mathematics and Physics focuses on numerical modelling of the atmospheres and oceans of terrestrial and giant planets. Currently, two 3D modelling systems are in use:
Isca
Isca is a framework for idealised modelling of the global circulation at varying levels of complexity. Isca was developed from models of Earth's atmosphere originally written at GFDL, but has been extended to allow simulation of other planetary regimes. A variety of atmospheric radiation, convection and surface schemes are available allowing a wide range of applications. The most sophisticated Isca configurations allow a direct connection to contemporary state-of-the-art general circulation models. Research at Exeter is led by Professor Geoff Vallis.
Idealised Met Office Unified Model
The Astrophysics group has adapted the Unified Model (UM), the numerical model used for weather forecasting and climate research by the UK Met Office, to simulate both rocky and giant "exoplanets" in orbit around other stars. Thousands of exoplanets have now been identified in our galaxy, and work with the UM aims to characterise their possible atmospheres and oceans in order to help interpret observations that will be made with new telescopes in the coming decades. This work has occurred in close collaboration with the UK Met Office. Research at Exeter is led by Dr Nathan Mayne, Dr Eric Hebrard and Dr Hugo Lambert.
Computational architecture
Both Isca and the UM are run on a variety of systems, depending on the computational demands of the problem under investigation. We use local servers for testing and model development, and Exeter University's own HPC facility also known as Isca, the UK Met Office collaboration cluster MonSOON and national facilities such as ARCHER and DiRAC for computationally intensive tasks.
Direct Numerical Simulations and Large Eddy Simulations
HPC Related
Projects and Collaborations
The following are some of the many projects and collaborative work we undertake.
DDE-BIFTOOL is an open-source library of routines for performing numerical bifurcation analysis of delay-differential equations, running in Matlab or Octave. It was originally created at KU Leuven (Belgium). Jan Siber is current lead maintainer and developer.
The weather and climate forecasts produced by the Met Office are underpinned by enormously complex numerical models running on state of the art supercomputers. Both physical accuracy and computational efficiency are critical for these operational applications. We have been collaborating with the Met Office for over a decade helping to develop the numerical methods and algorithms at the heart of their models.