Hi there! My name’s Jonathan! I’m a recent Master’s graduate from the University of Waterloo, and a soon-to-be PhD student at <insert university here>. My research interests involves simulating fluid flow in a realistic manner.


Master of Mathematics in Computer Science
2018 - (2020)
University of Waterloo

Ongoing degree under the supervision of Dr. Christopher Batty
Currently holding a 94% GPA

Honours Bachelor of Science in Integrated Science: Math and Stats Concentration with Physics Minor
2014 - 2018
McMaster University

Summa Cum Laude
Received an 11.9 GPA on a 12-point scale


Symposium on Computer Animation 2020

Jonathan Panuelos, Ryan Goldade, Christopher Batty


Unsteady Stokes solvers, coupling stress and pressure forces, are a key component of accurate free surface simulators for highly viscous fluids. Because of the simultaneous application of stress and pressure terms, this creates a much larger system than the standard decoupled approach. We propose a reduced fluid model wherein interior regions are represented with incompressible polynomial vector fields. Sets of standard grid cells are consolidated into super-cells, each of which are modelled using only 26 degrees of freedom. This reduced model retains desirable behaviour of the full Stokes system with smaller computational cost.

Journal of Computational Physics
Volume 414

Jonathan Panuelos, James Wadsley, and Nicholas Kevlahan


We present the first application of a central scheme in an unstructured meshless code and extend it to limit diffusion in shearing flows.
Some numerical diffusion is required in simulations of compressible fluids to maintain stability and prevent formation of spurious structures. The Kurganov-Tadmor (KT) central scheme uses a signal velocity and a linear reconstruction of fields to limit numerical diffusion away from discontinuities.
We implement the KT scheme as a drop-in replacement for the Riemann solver in the GIZMO hydrodynamics code. Both the original finite-volume version of the KT scheme, which is quasi-Lagrangian in meshless geometry, as well as a new fully-Lagrangian finite-mass variant are presented. In addition, to mitigate excessive diffusion, a new shear-based switch is proposed. The new methods, as well as the default Riemann solver, were applied to a set of test problems. The results show that, although the KT scheme is more diffusive than the Riemann solver, it produces correct results with better convergence. The switch is shown to reduce diffusion in shearing cases, while not compromising stability in the supersonic regime. The fully-Lagrangian variant is shown to behave similarly to its Riemann solver counterpart. We conclude that the new variants of the KT scheme are good alternatives to Riemann solvers in meshless geometry, especially where its simplicity is desirable, such as for a complex equation of state.

Research Positions

NSERC USRA: Numerical Methods in Hydrodynamics
May 2017 - Aug 2017
McMaster University

1-semester Undergraduate Student Research Award funded by the Natural Sciences and Engineering Research Council of Canada.
Analyzed and developed central-upwinding schemes in meshless finite-volume and finite-element applications.

NSERC USRA: Hydrodynamics Simulations
May 2016 - Aug 2016
McMaster University

1-semester Undergraduate Student Research Award funded by the Natural Sciences and Engineering Research Council of Canada.
Performed various fluid dynamics test cases using Gasoline and GIZMO simulation code.


Central Schemes and Shearing Diffusion in Particle Methods
Apr 2018
iSci Synthesis Conference 2018
Hamilton, ON, Canada

20-minute undergraduate thesis presentation on improving shearing diffusion in central schemes for meshless geometries.


Computational hydrodynamics is significant in the study of physical phenomena in astronomy, with the bulk of the universe’s matter being low-density gas.The Kurganov-Tadmor (KT) central scheme is a robust numerical flux scheme that performs well in simulating compressible fluids. It performs admirably at the supersonic regime, but is found to cause excessive diffusion, especially in the case of shearing problems. Diffusion is required to maintain stability and prevent formation of spurious structures, but too much suppresses even physically relevant structures.
A new method of controlling the diffusion in the KT scheme is proposed, based on determining whether the local flow is shearing or not. This is shown to be effective at reducing diffusion while retaining stability through an implementation in the GIZMO hydrodynamics code, which uses an unstructured geometry where fluid is simulated by representing it as a collection of particles whose movement represents the flow.
The method was tested using a range of problems, focusing on its behaviour in both shearing flows as well as in the supersonic regime. Results show that diffusion is noticeably reduced in shearing cases, while stability is not impacted in the supersonic regime. Additionally, it was shown to perform on-par with, or better than, other methods in a difficult test containing both shearing and supersonic components. Thus, the new method achieves the desired reduction of diffusion while maintaining the robustness of the KT scheme.

Stability and Artificial Viscosity in Numerical Hydrodynamics
Oct 2017
Canadian Undergraduate Physics Conference 2017
Ottawa, ON, Canada

10-minute oral presentation on the balance between numerical diffusion and stability in hydrodynamics simulations.


Numerical hydrodynamics attempts to capture the behaviour of physical fluid flow via numerical computation. The Euler fluid equations are the most commonly used mathematical representation of inviscid, compressible fluids, and one method of computing its solution numerically is called the Kurganov-Tadmor (KT) central scheme. Because of the limits of numerical analysis, however, challenges arise when attempting to solve ill-conditioned problems. Of interest are two such cases: singular gradients found in shocks, and the incompressible limit. Artificial viscosity is often used to stabilize methods in these ill-conditioned situations, but provides a challenge in determining how much is enough for stability, but not so much as to dominate over the physical result. An iterative improvement of the KT scheme will be presented, where a preconditioning method is applied to minimize the viscosity applied at subsonic cases, but keep its current stability in the supersonic regime.

Central Upwind Schemes in Smoothed Particle Hydrodynamics
Apr 2017
iSci Synthesis Conference 2017
Hamilton, ON, Canada

10-minute oral presentation on the implementation of the Kurganov-Tadmor central scheme into GIZMO.


Smoothed particle hydrodynamics (SPH) is a numerical method for solving Euler’s fluid equations. Originally developed for simulating gases in astrophysics, it has found uses in other fields including fluid flows and rigid body physics. SPH defines physical properties – density, velocity, and pressure – at points that follow the fluid field. These physical properties are used to interpolate values for the entire space. This interpolation, however, is inexact and leads to numerical errors in the calculation of momentum and energy fluxes between the particles. Methods for improving this error based off literature was assessed, and planned to be implemented into the SPH code, Gasoline.
A common, accurate class of methods for calculating fluxes are Riemann solvers. Due to their computational expense, however, they render simulations prohibitively slow in some cases – a faster, and possibly sufficiently accurate, alternative is the Kurganov-Tadmor (KT) central scheme. The KT scheme was initially used for grid simulations, thus making the upcoming implementation novel among SPH codes. It has been implemented into the hydrodynamics code, GIZMO, which currently uses a Riemann solver; and its viability will be analyzed via the use of standard test cases, where the KT scheme will be compared against that of a Riemann solver. Initial results are promising, but changes will be made due to the differences between grid codes and SPH. The implementation of the Kurganov-Tadmor central scheme into SPH is expected to yield improved results – accuracy close to exact Riemann solvers at significantly faster speeds.

When Bad Things Happen to Good SPH
Oct 2016
Canadian Undergraduate Physics Conference 2016
Halifax, NS, Canada

10-minute oral presentation on artificial viscosity and conductivity for resolving shocks in hydrodynamics simulations. Received third place award out of 14 talks in the astrophysics category.


Smoothed particle hydrodynamics (SPH) is a numeric computational method commonly used in astrophysics simulations, where physical properties are defined at points whose coordinates track the flow of the fluid rather than at a grid as is with a mesh-based method. Physical properties, such as density, pressure, and temperature, are interpolated from the values defined at nearby points using a smoothing function. As with any numerical solution, however, SPH has difficulty with mathematical singularities - of particular importance in hydrodynamics are shocks, discontinuities across which entropy increases. These can be seen in real life as waves produced by explosions and supersonic aircraft. Results for these discontinuities have traditionally been improved via the addition of an artificial viscosity, smearing it into a resolvable continuous curve. The behaviour of SPH on shocks of various strengths is analyzed, using varying degrees of artificial viscosity, as well as the effect of additional shock-specific thermal conduction. It was found that this addition yielded an improvement to shock results, but minor variations to the formulation were necessary to prevent detrimental effects on other cases, particularly shearing flows.

The Deterministic and Stochastic Lotka-Volterra Models
Apr 2016
iSci Synthesis Conference 2016
Hamilton, ON, Canada

Poster presentation to 120 peers and professors
Demonstrated a working simulation and summarized results of the Stochastic Lattice Lotka-Volterra Model in poster format.


A pioneering and now ubiquitous model in population ecology, the Lotka-Volterra system describes the temporal dynamics of two interacting species as a pair of differential equations. While mathematically elegant, it suffers from being deterministic, demonstrating the periodicity of predator-prey relationships, but little else. Its simplicity prevents more thorough analysis and generalization for more complex ecosystems, calling for a more robust analogue.
The inaccuracies in classical Lotka-Volterra largely stem from its lack of discrete, spatial, and stochastic elements – a more modern model, applying these corrections, is the Stochastic Lattice Lotka-Volterra, which treats the deterministic rates as probabilities applied over a discrete N×N lattice. As the same interactions defined by classical Lotka-Volterra are performed a large number of times, it becomes a Monte Carlo approximation, with probabilities being equivalent to rates at the mean-field limit.
Applying this new model in C, my analysis finds that while it approximates classical Lotka-Volterra, it exhibits more consistency with known ecological theory. In particular, it demonstrates decreasing fluctuation amplitude over time, as well as a bifurcation between the coexistence and extinction states, whereas the classical model implies an inevitable, perfectly periodic, coexistence for any two-species system.
Novel modifications to the simulation provides insight into the spatiotemporal behaviours of different ecosystems, such as species invasiveness and a parity law in trophic interactions. Thus, by applying the Lotka-Volterra model in silica, with the inclusion of discrete, spatial, and stochastic elements, a more accurate and robust model is created, applicable for the study of a wider range of ecosystems.


Ontario Graduate Scholarship
Province of Ontario | University of Waterloo

Merit-based scholarship and funding source for highly qualified graduate students in research-based programs.

NSERC Canada Graduate Scholarships - Master's
Natural Sciences and Engineering Research Council of Canada | University of Waterloo

Merit-based scholarship and funding source for highly qualified graduate students in research-based programs. Awarded at a maximum of once for a master’s degree.

President's Graduate Scholarship
2019, 2018
University of Waterloo
$8000 each
Math Domestic Master's Scholarship
University of Waterloo
Provost's Honour Roll Medal
McMaster University

Presented for achieving a 12.0 sessional GPA on a 12-point scale

George P. and Leatha M. Keys Scholarship
2017, 2016
McMaster University

Outstanding achievement in the Department of Math and Stats; Awarded per year

Dr. Harry Lyman Hooker Scholarship
2017, 2016, 2015
McMaster University

Awarded to top 10% of faculty per year

McMaster President's Award
McMaster University

Entrance Scholarship for 95% and above average

Teaching Experience

Teaching Assistant: CS 251
Sept 2020 - Dec 2020
University of Waterloo

Marking TA for CS 251: Computer Organization & Design
Responsibilities include marking student work and proctoring exams.

Instructional Apprentice: CS 251
Jan 2019 - Aug 2020
University of Waterloo

Instructional Apprentice (IA) for CS 251: Computer Organization & Design
Position held for 5 three-month terms
Responsibilities include holding office hours, answering student questions regarding course material, monitoring online course message board, organizing marking TAs, and marking remark requests.

Teaching Assistant: CS 115
Sept 2018 - Dec 2018
University of Waterloo

Marking TA for CS 115: Introduction to Computer Science 1
Responsibilities include marking student work and proctoring exams.

Teaching Assistant: ISCI 1A24 Physics
Sept 2016 - Apr 2017
McMaster University

TA under Dr. Nick Miladinovic for first year physics
Responsibilities include supervising labs, holding office hours, teaching tutorials, and marking student work.

Volunteer Experience

Promotions Manager and Webmaster
Sept 2017 - Aug 2018
The iScientist Undergraduate Journal

Member of the Editorial Board for the iScientist student-run journal, responsible for performing webmaster duties as well as maintaining social media pages and developing promotional graphics. Developed a new webpage for the journal using modern responsive design.

Mathematics and Physics Peer Tutor
Sept 2016 - Apr 2018
Integrated Science Program, McMaster University

Volunteer tutor at the iSci Peer Mentorship program, providing help with first and second year math and physics content.
Courses include ISCI 1A24 Math and Physics, ISCI 2A18 Math and Physics, MATH 1B03, MATH 2C03, MATH 2XX3, PHYSICS 2G03, PHYSICS 2B03.

Student Ambassador: Ontario University Fair
Sept 2017
Integrated Science Program, McMaster University

Volunteer ambassador representing the McMaster Integrated Science program at the Ontario University Fair 2017, wherein I spoke with and answered questions by prospective undergraduate students regarding the program;

3D Printing Workshop Co-Organizer
Apr 2017
iSci Synthesis Conference 2017

Coordinated with the Sherman Centre for Digital Scholarship to create an introduction to 3D printing workshop open to the public.

Arduino Workshop Presenter
Apr 2017
iSci Synthesis Conference 2017

Organized and presented a 2-hour introduction to Arduino workshop in McMaster’s Thode Makerspace. Position involved sourcing required electronics components, preparing a PowerPoint presentation, and promoting the event via posters and social media.

Space Exploration Planetarium Mentor
Mar 2017
iSci Highschool Workshop 2017

Gave guidance on the organization of the planetarium workshop, as well as held administrative duties involving event logistics.

Arduino Workshop Co-Organizer
Mar 2016
iSci Synthesis Conference 2016

Organizer for a publicly open 1-hour introductory workshop to the Arduino hardware platform. Responsibilities included working with the colloquium organizers for time and room bookings, contacting Dr. Jay Brodeur as the guest lecturer, and designing posters for event promotion.

Space Exploration Planetarium Presenter
Mar 2016
iSci Highschool Workshop 2016

Presented two 20-minute planetarium shows to a 25-student audience on interplanetary travel and the search for exoplanet life, highlighting various terrestrial bodies in the solar system.

Workshop Volunteer
Mar 2015
iSci Highschool Workshop 2015

Assisted directing high school students to workshop locations, as well as in workshop setup and cleanup.