My main research interests are in numerical solutions to nonlinear partial differential equations (PDEs) governing geophysical fluid flows, from models of large-scale ocean circulation to models of internal waves in lakes.
I continue to use a wide range of numerical techniques and strive to use the one most appropriate for a given problem. Methods I’ve used include (but are not limited to): Finite Difference Methods, Chebyshev and Fourier Spectral/Pseudospectral Methods, and the Discontinuous Galerkin Finite Element Method.
Although it is not my main focus, I often find myself fascinated by the various trade-offs one encounters when using Numerical Linear Algebra techniques to solve the large (sometimes dense) systems of equations that result from spatially discretizing a PDE. I also have interest in data assimilation and the application of stochastic differential equations (SDEs) to simple climate models.
Fluids group talk, Fall 2016: On Fractional-Step Schemes for Incompressible Inviscid Flow
PhD Thesis (title: “High-Order Numerical Methods in Lake Modelling”)
Fluids group talk, Fall 2013: Calculating free modes of oscillation in complex geometries
Gene Golub Siam Summer School 2012 Poster Presentation: High-Order Curvilinear Element Methods in Lake Modelling
Fluids group talk, Fall 2012: Dealing with insignificant fast waves in numerical models: Kinematic constraints vs. implicit time-stepping
Ph.D. Project Proposal, Spring 2010: Modelling Internal Wave Dynamics using Unstructured Grids (Note that animations won’t work, I may put them up here later)
CMOS 2010 Poster Presentation: High-Order methods for weakly nonhydrostatic layered models (Winner, Campbell Scientific Student Award)
Master’s Thesis (topic: Separating western boundary currents and the “beta-effect”).
D.T. Steinmoeller, M. Stastna, and K.G. Lamb. Discontinuous Galerkin Methods for Dispersive Shallow Water Models in Closed Basins: Spurious eddies and their removal using curved boundary methods, Ocean Modelling, 107: 112-124, 2016. doi 10.1016/j.ocemod.2016.10.007, pre-print pdf
S.M. Joshi, P.J. Diamessis, D.T. Steinmoeller, M. Stastna, and G.N Thomsen. A post-processing technique for stabilizing the discontinuous pressure projection operator in marginally-resolved incompressible inviscid flow, Computers & Fluids, 139: 120-129, 2016. doi 10.1016/j.compfluid.2016.04.021, arXiv pre-print
D.T. Steinmoeller, M. Stastna, and K.G. Lamb. A short note on the discontinous Galerkin discretization of the pressure projection operator in incompressible flow, Journal of Computational Physics, 251C: 480-486, 2013. doi 10.1016/j.jcp.2013.05.036, pre-print pdf
D.T. Steinmoeller, M. Stastna and K.G. Lamb. Pseudospectral methods for Boussinesq-type equations in an annular domain with applications to mid-sized lakes, Journal of Computational Science, 4: 3-11, 2012. doi 10.1016/j.jocs.2012.01.005, pre-print pdf
D.T. Steinmoeller, M. Stastna, and K.G. Lamb. On the evolution of a nonlinear, non-hydrostatic internal Kelvin wave in a stratified rotating circular basin, In: A. Cenedese (chair), Proceedings of the 7th International Symposium on Stratified Flows, 2011. pdf
D.T. Steinmoeller, S.J.D. D’Alessio, and F.J. Poulin. Prograde and retrograde flow past cylindrical obstacles on a β-plane, Acta Mechanica, 217(1): 157-176, 2011. doi 10.1007/s00707-010-0386-6, pre-print pdf
Links That Are Cool
Waterloo Quantitative Consulting Group (WQCG) - A consulting company that I started in Winter 2016.
crypt.ographer A website all about crypto and online security.
michaeljswart.com - Michael J. Swart’s blog. Lots of good information on databases.
Randall LeVeque’s homepage - A nice guy who writes books on numerical methods.
pysws - Procedural and Object-Oriented Python implementations for solving the shallow water equations with a Fourier pseudospectral method.
bandLimFourierInterp - A piece of software I’ve written for accurately interpolating periodic signals in 1D & 2D.
SPINWAVE - Fork of Chris Subich’s SPINS project that provides solvers for 1-layer and 2-layer weakly non-hydrostatic shallow water equations in periodic channel geometries.
UW Environmental and Geophysical Fluid Dynamics Group - Information about my research group (part of the Applied Math Department).
Continuum and Fluid Mechanics - Introductory materials for interested undergrads.
FluidsWiki - A compendium of fluids-related materials posted by fluids group members.
My TiCalc authors page - I wrote some BASIC programs when I was a teenager for Texas Instrument graphing calculators, but it looks like I lost the source code to them, booo!
This page was last updated on March 25, 2018. If you spot any broken links, please contact me with which link is broken and a suggestion for what the link should be referencing.