Fellow and Tutor, University Lecturer in Applied Mathematics
Dr Dellar is on sabbatical leave for the academic year 2016-2017.
Dr Dellar returned to Corpus in October 2007 as Tutor in Applied Mathematics, having been a lecturer in mathematics at Imperial College London. He was previously a Junior Research Fellow at Corpus from October 2001 until September 2004, while he held one of the University's Glasstone Research Fellowships. His earlier career as an undergraduate, graduate student, and then research fellow, was at the University of Cambridge. He is an alumnus of the Woods Hole Summer Study Programme in Geophysical Fluid Dynamics.
Dr Dellar 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. Dr Dellar creates microscopic models of colliding particles whose statistically averaged behaviour he 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 Dr Dellar's algorithms for magnetohydrodynamics is being developed into another software package for the nuclear industry.
Dr Dellar also works 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 Corpus DPhil student Andrew Stewart, Dr Dellar has 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.
Dr Dellar is also interested in many other things, including topics in scientific computation and further practical applications of mathematics in industry through the ``study group'' format.
Dr Dellar's 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 his research activities. He currently supervises research in lattice Boltzmann approaches to multiphase flow, and to quantum systems, and in the fluid dynamics of the Earth's ocean and Jupiter's atmosphere.
P. J. Dellar (2009) Moment equations in magnetohydrodynamics J. Stat. Mech. (2009) P06003
P. J. Dellar (2007) Macroscopic descriptions of rarefied gases from the elimination of fast variables Phys. Fluids 19 107101
P. J. Dellar and R. Salmon (2005) Shallow water equations with a complete Coriolis force and topography Phys. Fluids 17 106601
P. J. Dellar (2004) Quasi-two-dimensional liquid metal magnetohydrodynamics and the anticipated vorticity method J. Fluid Mech. 515 197-232
P. J. Dellar (2002) Lattice kinetic schemes for magnetohydrodynamics J. Comput. Phys. 179 95-126
see http://people.maths.ox.ac.uk/~dellar/ for links