Collin
Wittenstein

Geothermal Well Simulations

Deep borehole heat exchangers extract geothermal energy by circulating fluid through closed-loop pipes that extend several kilometers into the Earth. This sounds nice, but simulating them is unfortunately not easy: you're dealing with multi-scale geometry where boreholes are centimeters wide but kilometers deep, and you need to simulate years to decades of operation to understand thermal performance. For arrays of multiple wells interacting thermally over these timescales, it was traditionally thought that a fully three-dimensional simulation of the arrays would be computationally prohibitive. Luckily for me I didn't know this before starting to work on the project.

So, I developed a GPU-accelerated three-dimensional model simulating geothermal well arrays. The key innovation is an operator splitting strategy tailored to the problem's physics. Vertical diffusion gets stabilized explicit Runge-Kutta-Chebyshev methods, horizontal diffusion gets ADI schemes, advection gets semi-Lagrangian treatment. Each operator handled by whatever works best for it - sounds obvious in hindsight, but figuring out this combination took a while.

I released this as the open-source Julia package GeothermalWells.jl, using vendor-agnostic GPU kernels that run on both NVIDIA and AMD hardware. Full three-dimensional simulations of multi-well arrays over decades can now run on a single GPU, enabling systematic design space exploration and optimization of geothermal well systems.

On a single NVIDIA H200, simulating 20 years of operation of a 5×5 array of 25 wells takes about 15 hours, so the whole lifetime of a large well field fits into roughly half a day. Usually this is where people compare their runtime to other codes. But there are no other fully three-dimensional simulations of whole well arrays to compare against, so this number has to stand on its own.

This became my master's thesis, supervised by Prof. Hendrik Ranocha and Prof. Friederike Schmid, and done in collaboration with Prof. Alan Edelman and Robert Metcalfe at MIT – who also wrote the foreword.

Water Wave Simulations

I worked on dispersive shallow water equations. The following visualization shows the evolution of a wave over Gaussian bathymetry, using the hyperbolic approximation of the Serre–Green–Naghdi (SGN) equations in two dimensions. The simulation employs a new energy-conserving semi-discretization that maintains physical properties over long time integrations. Since the hyperbolic approximation avoids the elliptic solves of the original equations, everything maps nicely onto GPUs. Together with some careful engineering of the GPU kernels, this makes the method faster than state-of-the-art open-source GPU solvers for the SGN equations, while running in double precision and conserving energy exactly. Turning math into fast code, as promised. I also worked quite a bit on DispersiveShallowWater.jl, a Julia package that implements structure-preserving numerical methods for one-dimensional dispersive shallow water models. Supervised by Prof. Hendrik Ranocha.

Rattleback Simulation

For my bachelor's thesis in mathematics, I simulated the movement of the rattleback (German: Wackelstein), a semi-ellipsoid with an inhomogeneous mass distribution that exhibits quite counterintuitive behavior: it can spontaneously reverse its spinning direction. This phenomenon defies intuition but follows directly from the solutions of its equations of motion. Supervised by Prof. Hendrik Ranocha and Prof. Elmar Schömer.

For this work, I received the best bachelor's thesis in mathematics of the year award.