Spectral methods for PDEs with Dedalus
I'm the lead developer of Dedalus, an open-source framework for solving differential equations with modern spectral methods. Dedalus is composed of generalized algorithms that can accomodate a broad range of custom equation sets and spectral domains. It's written in Python 3 and is easy to use on a laptop, yet calls compiled libraries for performance-critical routines and can scale to thousands of cores with MPI.
One of the core components of Dedalus is a parser I developed to transform sets of equations, algebraic constraints, and boundary conditions from plain text into a sparse tau/Galerkin formulation. This mathematical formulation is based on work led by Geoff Vasil on constructing flexible systems of sparse operators on Jacobi polynomials. Other aspects of the codebase are influenced by an MHD shearing-box code I developed with Jeff Oishi.
Nonlinear tides in astrophysical bodies
In collaboration with my advisor Nevin Weinberg, I'm investigating the nonlinear stability and saturation of tides in giant planets, stars, and compact objects. Orbiting bodies generate tides in their companions, and the dissipation of these tides can modify the orbital evolution of such systems over time. We're using direct numerical simulations to test theories of nonlinear instabilities and estimates of tidal dissipation rates in systems such as hot Jupiters and neutron-star binaries.
Glacial meltwater plumes
In collaboration with Andrew Wells and my advisor Glenn Flierl, I'm using Dedalus to model turbulent flows at the edges of marine-terminating glaciers. The fresh melt from the submerged face of such glaciers is buoyant with respect to the surrounding fluid, and forms a rising plume along the glacier's edge. The turbulent characteristics of these plumes may ultimately control the heat transport between the ambient water and the glacier, thereby influencing the melt rate and evolution of the glacier.
Rolling resistance on granular media
In collaboration with Neil Balmforth and Ian Hewitt, I'm studying the dynamics of rolling objects on sand and other granular materials. This project began with experiments I performed as a fellow in the 2016 Geophysical Fluid Dynamics program at the Woods Hole Oceanographic Institute.
This image shows some of the hundreds of trajectories we recorded of various cylinders rolling over sand and glass beads in the WHOI GFD laboratory.
"Turbulent Chemical Diffusion in Convectively Bounded Carbon Flames"
Lecoanet et al., Astrophysical Journal, 2016. [ADS] [DOI]
"Tensor calculus in polar coordinates using Jacobi polynomials"
Vasil et al., Journal of Computational Physics, 2016. [ADS] [DOI]
"A validated nonlinear Kelvin-Helmholtz benchmark for numerical hydrodynamics"
Lecoanet et al., MNRAS, 2016. [ADS] [DOI]
"Numerical simulations of internal wave generation by convection in water"
Lecoanet et al., Physical Review E, 2015. [ADS] [DOI]
"Conduction in Low Mach Number Flows. I. Linear and Weakly Nonlinear Regimes"
Lecoanet et al., Astrophysical Journal, 2014. [ADS] [DOI]
"FIRST, a fibered aperture masking instrument. I. First on-sky test results"
Huby et al., Astronomy & Astrophysics, 2012. [ADS] [DOI]
"Sidewall-driven convection in a thermally and compositionally stratified fluid"
Burns et al., APS DFD, 2016. [PDF] [ADS]
"Turbulent structures in convection from a heated sidewall in a stratified fluid"
Burns et al., APS DFD, 2015. [PDF] [ADS]
"Numerical simulations of nonlinear wall-mode convection"
Burns et al., AGU Fall Meeting, 2014. [PDF] [ADS]
"Orbital Stability of Spacecraft Exploring Multiple Asteroid Systems"
Burns et al., AAS 218th Meeting, 2011. [PDF] [ADS]