Relativistic Hydrodynamics with Wavelets

DeBuhr, Jackson; Zhang, Bo; Anderson, Matthew; Neilsen, David; Hirschmann, Eric W.; Grenga, Temistocle; Paolucci, Samuel

doi:10.3847/1538-4357/aae5f9

Relativistic Hydrodynamics with Wavelets

Journal Article · Tue Nov 06 00:00:00 EST 2018 · The Astrophysical Journal (Online)

DOI:https://doi.org/10.3847/1538-4357/aae5f9· OSTI ID:1614513

DeBuhr, Jackson ^[1]; Zhang, Bo ^[2]; Anderson, Matthew ^[2]; Neilsen, David ^[3]; Hirschmann, Eric W. ^[3]; Grenga, Temistocle ^[4]; Paolucci, Samuel ^[5]

Indiana Univ., Bloomington, IN (United States); DOE/OSTI
Indiana Univ., Bloomington, IN (United States)
Brigham Young Univ., Provo, UT (United States)
RWTH Aachen Univ. (Germany)
Univ. of Notre Dame, IN (United States)

Methods to solve the relativistic hydrodynamic equations are important in a large number of astrophysical simulations, which may be very dynamic and involve multiscale features. This requires computational methods that are highly adaptive and capable of automatically resolving numerous localized features and instabilities that emerge across the computational domain and over many temporal scales. While this has been historically accomplished with adaptive-mesh-refinement-based methods, alternatives using wavelet bases and the wavelet transformation have recently achieved significant success in adaptive representation for advanced engineering applications. The current work presents a new method, extending the wavelet adaptive multiresolution representation method, for the integration of the relativistic hydrodynamic equations using iterated interpolating wavelets and introduces a highly adaptive implementation for multidimensional simulation. We note 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 1D and 2D problems that explore high Lorentz factor outflows and the formation of several instabilities, including the Kelvin–Helmholtz instability and the Rayleigh–Taylor instability.

View Accepted Manuscript (DOE)

Research Organization:: Indiana Univ., Bloomington, IN (United States); Univ. of Notre Dame, IN (United States)

Sponsoring Organization:: National Aeronautic and Space Administration (NASA); National Science Foundation (NSF); USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: NA0002377; SC0008809

OSTI ID:: 1614513

Journal Information:: The Astrophysical Journal (Online), Journal Name: The Astrophysical Journal (Online) Journal Issue: 2 Vol. 867; ISSN 1538-4357

Publisher:: Institute of Physics (IOP)Copyright Statement

Country of Publication:: United States

Language:: English

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