MrElliot Badcock

I am a doctoral researcher in the Department of Mathematics at Imperial College London, investigating efficient numerical approximation methods for boundary layer stability analysis under the supervision of Dr. Shahid Mughal. My research addresses the fundamental challenge of reconciling asymptotic theory with practical numerical implementation for fluid dynamics problems, with particular emphasis on laminar-turbulent transition prediction.

My doctoral thesis, "Efficient Spatial Marching for Boundary Layer Stability: From PSE to OWNS and the Development of Modal-OWNS," systematically advances spatial marching methodologies for approximating solutions to the elliptic Navier-Stokes equations. I have developed leading-order asymptotic models for disturbance propagation in three-dimensional boundary layers (PSE3D), formulated rigorous mathematical justification for numerical schemes through characteristic analysis, and pioneered the novel Modal One-way Navier-Stokes (M-OWNS) approach that demonstrably enhances convergence characteristics while reducing computational complexity by a factor of 80-120× compared to conventional OWNS implementations.

This research has practical applications for complex aerodynamic configurations, as evidenced by my collaborative work with the Defence Science and Technology Laboratory applying advanced stability methods to the SWiFT model, a transonic wind tunnel configuration developed under NATO Science and Technology Organisation's Research Task Group 298.

I commenced my doctoral studies in August 2021 after obtaining an MMath with First Class Honours from Cardiff University (2014-2018), where my Master's thesis focused on Spectral Theory and Functional Analysis under the supervision of Professor Karl Schmidt. Between my undergraduate and doctoral studies, I served as a mathematics teacher at Wembley High Technology College (2018-2021), teaching A-Level Mathematics and Further Mathematics whilst developing specialist curricula and mentoring departmental colleagues.

My technical expertise encompasses object-oriented Fortran, MATLAB, Python, parallel computing methodologies, and advanced numerical analysis techniques including high-order finite difference and spectral discretisation schemes, efficient eigenvalue solvers, and asymptotic analysis for partial differential equations. This computational foundation enables the development of sophisticated numerical frameworks for complex fluid dynamics problems.

My doctoral research is funded by the Defence Science and Technology Laboratory.