My research focuses on modelling and numerical methods for energy systems. My PhD was centered around the modelling of LiFePO4, a battery chemistry that can undergo a phase change during charge/discharge. Solving the large, coupled systems of nonlinear PDEs that result requires the use of appropriate discretisation methods (such as finite volume) along with parallel, Newton-Krylov schemes and extensive validation and verification against experimental data.
My postdoctoral research is based on developing numerical methods for Boltzmann transport applications, including civil nuclear, coupled CFD/radiative transfer, lattice Boltzmann, spectral wave, etc. These include adaptive schemes and error metrics, FEM and wavelet based discretisations across the space/angle/energy phase-space and large-scale parallelism.
et al., 2020, Goal-based angular adaptivity for Boltzmann transport in the presence of ray-effects, Journal of Computational Physics, Vol:421, ISSN:0021-9991, Pages:1-19
et al., 2020, Scalable angular adaptivity for Boltzmann transport, Journal of Computational Physics, Vol:406, ISSN:0021-9991, Pages:1-32
et al., 2019, Angular adaptivity with spherical harmonics for Boltzmann transport, Journal of Computational Physics, Vol:397, ISSN:0021-9991, Pages:1-19
Dargaville S, Farrell TW, 2015, A least squares based finite volume method for the Cahn-Hilliard and Cahn-Hilliard-reaction equations, Journal of Computational and Applied Mathematics, Vol:273, ISSN:0377-0427, Pages:225-244
Dargaville S, Farrell TW, 2013, A comparison of mathematical models for phase-change in high-rate LiFePO4 cathodes, Electrochimica Acta, Vol:111, ISSN:0013-4686, Pages:474-490
Dargaville S, Farrell TW, 2013, The persistence of phase-separation in LiFePO4 with two-dimensional Li+ transport: The Cahn-Hilliard-reaction equation and the role of defects, Electrochimica Acta, Vol:94, ISSN:0013-4686, Pages:143-158
Dargaville S, Farrell TW, 2010, Predicting Active Material Utilization in LiFePO4 Electrodes Using a Multiscale Mathematical Model, Journal of the Electrochemical Society, Vol:157, ISSN:0013-4651, Pages:A830-A840