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.

Undular bore kelvin wave train Lake Opeongo Rings

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.


Google Scholar Page

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”).

Selected Publications

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/, pre-print pdf

D.T. Steinmoeller, M. Stastna and K.G. Lamb. Fourier pseudospectral methods for 2D Boussinesq-type equations, Ocean Modelling, 52-53: 76-89, 2012. doi 10.1016.j.ocemod.2012.05.003, 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. - 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!



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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.