Relativistic Computational Fluid Dynamics

On Relativistic Computational Fluid Dynamics

Fluid simulations is the process in which the behavior of fluids, which can be represented by physical laws of mass, momentum and energy conservation, are put into a discretized form which approximates the continuum behavior. Since the partial differential equations governing fluid flow are nonlinear and have a number of problematic features, this is by no means a straightforward procedure, and it has taken many years for a number of overall reliable algorithms to emerge.

If the fluid is also coupled to an electromagnetic field, the situation gets more complicated. In practice, an approximation called the ideal MHD equations is often used, particularly for plasma flows in astrophysics. The coupled nature of the fluid flow and Maxwell's field equations governing the electromagnetic field changes the local characteristic spectrum of the equations, which is associated with new coupled wave types (Alfvén and magnetosonic waves).

Add another two levels of complication by going to general relativistic flows: Einstein's theory of general relativity describes the universe as a curved spacetime manifold, where each local observer perceives his immediate environment to be governed by the laws of special relativity. The latter introduces the speed of light as a fundamental limit (and as an invariant) into the fluid flow, thereby introducing additional couplings and numerical complications, and the former complicates the situation in that we suddenly need to account for the intrinsic (and constantly changing) geometry of the spacetime.

My Activities

A lot of my professional research has centered around implementation and applications of relativistic computational fluid dynamics. The application side has involved simulations of astrophysical systems and events which require a general relativistic description, in particular neutron stars and black holes. On the implementation side, I have authored two complete simulation codes for general relativistic magnetohydrodynamics, the Thor and Horizon codes.

The Thor code is part of the Cactus computational infrastructure and employs so-called multiblock meshes to discretize the spatial domain. With these meshes, it becomes possible to obtain a smooth covering of spherical boundaries, a feat which is important when it comes to simulations of accretion disks around black holes.

The new Horizon code employs GPU computing to accelerate the simulations of relativistic fluid flow. Compared to Thor, it can be up over 50 times faster, which is a huge difference in practice. With this code, the first long-term studies of dynamical hydromagnetic instabilities inside the core of magnetars have been made possible for the first time.