I'm a computational mathematics researcher, with a focus on geophysical fluid dynamics, ocean modelling and planetary climate simulation. My research interests include: high-order accurate finite-volume/difference methods for computational fluid dynamics, general-circulation modelling and ocean dynamics, mesh-generation and computational geometry.

I work on both academic and industrial research projects.

I'm currently an Associate Research Scientist at Columbia University and the NASA Goddard Institute for Space Studies (NASA-GISS). I'm contributing to the development of a new high-resolution global ocean model for planetary climate simulation.

Sometimes, I try to explore more philosophical questions, through collaborations with my wife, artist Sara Morawetz.


Contact: darren [dot] engwirda [at] columbia [dot] edu


PROJECTS


See my github profile for a full listing.

JIGSAW-GEO: a variant of my general-purpose meshing library JIGSAW, designed to generate high-quality grids for unstructured ocean/atmospheric models, including MPAS, COMPAS, FESOM, ICON and PERISCOPE.

See JIGSAW-GEO on github for more >>

PERISCOPE: an unstructured, arbitrary lagrangian-eulerian ocean model.

PERISCOPE is still under development.

JIGSAW: a computational library for unstructured mesh generation; designed to generate high-quality triangulations and polyhedral decompositions of general planar, surface and volumetric domains.

See JIGSAW on github for more >>

PPR: a Fortran library for high-order Piecewise Polynomial Reconstruction (PPR). This package forms the basis for our high-order finite-volume and arbitrary lagrangian-eulerian (ALE) transport algorithms.

See PPR on github for more >>

MESH2D: a MATLAB / OCTAVE-based unstructured mesh-generator for two-dimensional polygonal geometries, providing a range of relatively simple, yet effective two-dimensional meshing algorithms.

See MESH2D on github for more >>



PUBLICATIONS


Multi-resolution unstructured grids for coastal ocean modelling via restricted Delaunay triangulations (D. Engwirda, 2017. In preparation.)

A description of JIGSAW's 'restricted' Delaunay algorithm for the approximation of coastal boundaries in unstructured grids.

Generalised primal-dual grids for unstructured co-volume schemes (D. Engwirda, 2018. J. Comp. Phys., 375, 155-176) https://doi.org/10.1016/j.jcp.2018.07.025

An algorithm for the construction of 'weighted' Delaunay/Voronoi pairs (a.k.a. Regular/Power tessellations) to build 'optimal' grids for co-volume schemes.

JIGSAW-GEO (1.0): locally orthogonal staggered unstructured grid generation for general circulation modelling on the sphere (D. Engwirda, 2017, Geosci. Model Dev., 10, 2117-2140) https://doi.org/10.5194/gmd-10-2117-2017

JIGSAW's spherical meshing algorithm; designed to generate high-quality unstructured grids for global ocean/atmospheric modelling.

High-order accurate finite-volume formulations for the pressure gradient force in layered ocean models. (D. Engwirda, M. Kelley, & J. Marshall, 2017, Ocean Modelling, 116, 1-15) https://doi.org/10.1016/j.ocemod.2017.05.003

A finite-volume formulation for the pressure-gradient force in 'generalised' coordinate ocean models.

Conforming restricted Delaunay mesh generation for piecewise smooth complexes.(D. Engwirda, 2016, Procedia Engineering, 163, 84-96 http://dx.doi.org/10.1016/j.proeng.2016.11.024

A description of JIGSAW's 'restricted' Frontal-Delaunay algorithm for meshing surfaces/volumes with 'sharp-features'.

Voronoi-based point-placement for three-dimensional Delaunay-refinement. (D. Engwirda, 2015, Procedia Engineering, 124, 330-342 http://dx.doi.org/10.1016/j.proeng.2015.10.143

A description of JIGSAW's 'off-centre' type Delaunay-refinement algorithm for meshing three-dimensional volumes.

On the formulation of environmental fugacity models and their numerical solutions. (M. Bates, M. Bigot, R. Cropp, D. Engwirda, C. Friedman & D. Hawker, 2016, Environmental Toxicology and Chemistry, 35 (9), 2182-2191 http://dx.doi.org/10.1002/etc.3403

A analysis of fugacity models, focusing on consistent, mass-based fomulations.

Off-centre Steiner points for Delaunay-refinement on curved surfaces. (D. Engwirda & D. Ivers, 2016, Computer-Aided Design, 72, 157-171 https://doi.org/10.1016/j.cad.2015.10.007

A description of JIGSAW's 'off-centre' type Delaunay-refinement algorithm for meshing curved surfaces.

Face-centred Voronoi refinement for surface mesh generation. (D. Engwirda & D. Ivers, 2014, Procedia Engineering, 82, 8-20 http://dx.doi.org/10.1016/j.proeng.2014.10.364

A brief description of JIGSAW's 'off-centre' type Delaunay-refinement algorithm for meshing curved surfaces.



REPORTS


Multi-resolution unstructured grid-generation for geospatial applications on the sphere, (D. Engwirda, Research Note, International Meshing Roundtable, 2015) arXiv preprint arXiv:1512.00307

Initial exploration of spherical mesh generation using JIGSAW.

A WENO-type slope-limiter for a family of piecewise polynomial methods, (D. Engwirda and M. Kelley, NASA Tech. Report, 2015) arXiv preprint arXiv:1606.08188

A description of the WENO-limited PQM/PPM reconstruction techniques used in our finite-volume and arbirary lagrangian-eulerian algorithms.

Locally-optimal Delaunay-refinement and optimisation-based mesh generation, (D. Engwirda, September 2014, Ph.D Thesis, School of Mathematics and Statistics, The University of Sydney) http://hdl.handle.net/2123/13148

My Ph.D. thesis, analysing various 'restricted' Frontal-Delaunay refinement algorithms and mesh-optimisation techniques.

Unstructured mesh methods for the Navier-Stokes equations, (D. Engwirda, November 2005, Undergraduate Honours Thesis, School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney)

My undergraduate honours thesis, describing an unstructured finite-volume type solver for the unsteady Navier-Stokes equations.



SCIENCE/ART WORKS (WITH SARA MORAWETZ)


étalon: [A performative walk in search of the metre]. We measure only by measuring against; a self-reflexive act of standardisation through which we order society [and self as a consequence]. To measure is to run from chaos; to divest oneself of natural entropy; to know space, place and purpose with certainty. By surveying the Paris meridian, Sara and a team of female artists will measure the Earth's curvature and create a new 'metre' through physical action.

61/60: [A series of 1-second performances celebrating leap-seconds]. The leap-second is the 'force' by which the sun is held overhead at midday, and without it our time would become unfastened to the solar-cycles in which it is steeped. Through haphazard and listless drift, we would eventually find the passage of our star bore little relation to the movement of our clocks. Striking a pair of cymbals coincident with each event, Sara tracks this unfolding discontinuity.

How the Stars Stand: [An investigation of time as measured on Mars]. Our experience of time is not constant, rather, it flexes and yields to the nature of our passage through space. Bound to Earth, this concept seems imperceptible, for we know no time but our own. Yet as we chart our path around the sun, revolving on a familial axis, time operates differently elsewhere. Living in open-source gallery for 36 Martian 'sols', Sara charted the divergence of planetary 'time'.