I returned to Corpus in October 2007 as Tutor in Applied Mathematics, having been a lecturer in mathematics at Imperial College London. I was previously a Junior Research Fellow at Corpus from October 2001 until September 2004, while I held one of the University's Glasstone Research Fellowships. My earlier career as an undergraduate, graduate student, and then research fellow, was at the University of Cambridge. I am an alumnus of the Woods Hole Summer Study Programme in Geophysical Fluid Dynamics.
Research and Teaching
My main research interests are in lattice Boltzmann approaches for simulating fluid dynamics, and for more exotic applications to electromagnetic and quantum systems. Originally inspired by the kinetic theory of gases, the lattice Boltzmann approach has recently become very popular because the microscopic models are very easy to implement on modern parallel computers. I create microscopic models of colliding particles whose statistically averaged behaviour I can show approaches the solution of the Navier-Stokes, Maxwell, or Dirac equations. Practical applications range from simulating blood flow through surgical stents to a software package widely used in the car industry. One of my algorithms for magnetohydrodynamics is being developed into another software package for the nuclear industry.
I also work on the fluid dynamics of the atmosphere and oceans, chiefly using shallow water descriptions derived from variational principles to study their large-scale behaviour. Along with a former Corpus DPhil student Andrew Stewart, I have derived shallow water equations with a better approximation to the Coriolis force experienced by a fluid moving on a rotating planet. They are using these equations to model the flow of deep ocean currents across the equator, such as how cold, deep water from Antarctica crosses the equator to reach the Caribbean, where it goes on to form the warm Gulf Stream that moderates the UK's climate despite its high latitude.
I am also interested in many other things, including topics in scientific computation and further practical applications of mathematics in industry through the 'study group' format.
My teaching of applied mathematics encompasses first and second year undergraduate tutorials on vector calculus, differential equations, calculus of variations, and electromagnetism, all topics that overlap with my research activities.
P. J. Dellar (2019) Relativistic properties and invariants of the Du Fort-Frankel scheme for the one-dimensional Schrödinger equation J. Comput. Phys. X 2 (2019) 100004
E. S. Warneford & P. J. Dellar (2017) Super- and sub-rotating equatorial jets in shallow water models of Jovian atmospheres: Newtonian cooling versus Rayleigh friction J. Fluid Mech. 822 484-511
A. L. Stewart & P. J. Dellar (2016) An energy and potential enstrophy conserving numerical scheme for the multi-layer shallow water equations with complete Coriolis force J. Comput. Phys 313 99-120
E. S. Warneford & P. J. Dellar (2014) Thermal shallow water models of geostrophic turbulence in Jovian atmospheres Phys. Fluids 26 016603
P. J. Dellar (2013) Lattice Boltzmann magnetohydrodynamics with current-dependent resistivity J. Comput. Phys. 237 115-131