Master's Thesis Defense by Jonas Ølshøj Pedersen

Title: Going with the Flow: Improving the fidelity of Lagrangian particles in tracing a Eulerian Fluid

Abstract: Eulerian models for hydrodynamics, which describe the physical evolution of fluids with a static grid discretization, are one of the most powerful tools in astrophysics for building models that can be used to interpret observations and improve our theoretical understanding of astrophysical phenomena. A limitation of the grid-based representation is that changes with time are incorporated into the model by incremental changes of quantities in individual cells, making it impossible to access the history of where mass comes from. To address this, passive Lagrangian tracer particles can be added to follow the flow of mass in the model. However, current tracer particle methods either struggle with accurately tracing the flow or suffer from stochastic noise. The choice of tracer particle method thus invites both benefits and problems, and this project revolves around determining those most suitable for astrophysical experiments.

This project uses a Eulerian MUSCL scheme with five different tracer particle implementations for tracing the hydrodynamics of three test problems: Fluid compression and expansion, the Kelvin-Helmholtz instability, and Driven Turbulence. In each test the evolution of errors in tracer particle densities is monitored carefully, and tested against varying system parameters.

It is found that tracer particles with well-behaved trajectories show difficulties in handling steep density gradients, as well as being unable to resolve the mixing of fluids. In contrast, tracer particles with an inherent stochasticity show far higher accuracy when meeting density gradients, as well as far better mixing, although at the cost of added noise. We conclude that particles combining both aspects could turn out far superior to the currently used tracers and present a first example of such particles.

Supervisors: Troels Haugbølle and Thomas Berlok, University of Copenhagen, Niels Bohr Institute

Censor: Steen Hannestad, Aarhus University