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Lagrangian tracer particles

In astrophysics and galaxy formation, the Euler equations for hydrodynamics are usually modeled with either Lagrangian methods (e.g. SPH) or Eulerian methods (e.g. AMR or moving-mesh). Both methods have their advantages and downsides. One of the downsides of Eulerian methods is that they do not readily allow to follow individual ‘fluid parcels’ as they move and mix in the computational domain.

However, some very interesting scientific questions can greatly benefit from an ability to follow the fluid from its initial configuration, through its various thermodynamical evolution stages, to its final configuration. To do that, ‘tracer particles’ have been implemented in various hydrodynamical codes. The most common approach for tracer particles implements them as massless particles that are advected with the fluid based on the local modeled velocity field. In my work, I have shown that this approach has basic conceptual flaws that prevent it from being able to reliably follow the fluid.

Instead, I and my collaborators have introduced a novel method, where tracer particles are associated with fluid cells, and are exchanged between them in correspondence to the mass exchanges (fluxes) between the cells. With this approach, the tracer particles are guaranteed to follow the fluid correctly on average, albeit with some shot noise and increased diffusion.