Implementation of Coupled In Situ Adaptive Tabulation (ISAT) and Nonlinear Dimensionality Reduction Methods in Reactive Systems.

Most industrial and environmental processes involve several multi-scale physical phenomena over a large range of time-scales. Such multi-physics (or fully-coupled) processes can involve, for example, transport of quantities (e.g., advection and diffusion of active/passive tracers, dispersion of pollutants in atmospheric or water systems), scattering of neutrons, chemical reactions, biological processes, solid mechanics (structure dynamics) etc.

In rapid chemistry processes, such as combustion, kinetics mechanisms are represented by a system of stiff ordinary differential equations (ODE) that need to be balanced and solved simultaneously. When such processes are coupled with transport equations (advection and diffusion processes), time- and spatial-scales need to be taken into account to accurately preserve mass conservation.
The ISAT is an adaptive search-retrieval-load algorithm in k-ary trees that has been used to speed up the solution of stiff ODEs. Nonlinear reduction methods (NMR) are based on linear projection of data into a lower-order dimension subspace. In this project ISAT and NMR will be integrated to efficiently solve systems of stiff ODEs representing chemical reactions.

The successful candidate should have, or expect to have, an Honours Degree at 2.1 or above (or equivalent) in mathematics, physics, computer science or chemical engineering, and have a strong interest in mathematical modelling, numerical analysis and computer programming. It is essential that candidates have experience using Linux. It is desirable, but not essential, that candidates have experience using HPC platform, programming (in Python and Fortran or C) and have an interest in computational fluid dynamics.