Relativistic Hydrodynamics with Wavelets

TL;DR

This paper introduces a novel wavelet-based method for solving relativistic hydrodynamic equations, offering high adaptivity and accuracy crucial for astrophysical simulations involving complex, multi-scale fluid phenomena.

Contribution

The work develops a new wavelet-based integration method for relativistic hydrodynamics and implements a highly adaptive multidimensional simulation code called OAHU.

Findings

Successfully applied to high Lorentz factor outflows.

Effectively captures fluid instabilities like Kelvin-Helmholtz and Rayleigh-Taylor.

Demonstrates improved adaptivity over traditional methods.

Abstract

Methods to solve the relativistic hydrodynamic equations are a key computational kernel in a large number of astrophysics simulations and are crucial to understanding the electromagnetic signals that originate from the merger of astrophysical compact objects. Because of the many physical length scales present when simulating such mergers, these methods must be highly adaptive and capable of automatically resolving numerous localized features and instabilities that emerge throughout the computational domain across many temporal scales. While this has been historically accomplished with adaptive mesh refinement (AMR) based methods, alternatives based on wavelet bases and the wavelet transformation have recently achieved significant success in adaptive representation for advanced engineering applications. This work presents a new method for the integration of the relativistic hydrodynamic equations using iterated interpolating wavelets and introduces a highly adaptive implementation for multidimensional simulation. The wavelet coefficients provide a direct measure of the local approximation error for the solution and place collocation points that naturally adapt to the fluid flow while providing good conservation of fluid quantities. The resulting implementation, OAHU, is applied to a series of demanding one- and two-dimensional problems which explore high Lorentz factor outflows and the formation of several instabilities, including the Kelvin-Helmholtz instability and the Rayleigh-Taylor instability.