Relativistic hydrodynamics with wavelets
Relativistic hydrodynamics with wavelets
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. 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.
gamma-ray burst: general, hydrodynamics, methods: numerical, relativistic processes
Debuhr, Jackson
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Zhang, Bo
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Anderson, Matthew
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Neilsen, David
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Hirschmann, Eric W.
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Grenga, Temistocle
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Paolucci, Samuel
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10 November 2018
Debuhr, Jackson
c26fcce2-c524-413c-a6d0-1e72c8842a4f
Zhang, Bo
b4357fc4-109b-4499-a865-ad0b2386c076
Anderson, Matthew
c3c9c639-8fca-46d3-bda3-a56fadeaa59e
Neilsen, David
f1187d99-0b22-4126-830a-0d238e32e680
Hirschmann, Eric W.
2dd68f74-c005-4d42-a2be-894dc3874a5f
Grenga, Temistocle
be0eba30-74b5-4134-87e7-3a2d6dd3836f
Paolucci, Samuel
d9d7b875-1826-43d8-8058-c48802001e29
Debuhr, Jackson, Zhang, Bo, Anderson, Matthew, Neilsen, David, Hirschmann, Eric W., Grenga, Temistocle and Paolucci, Samuel
(2018)
Relativistic hydrodynamics with wavelets.
Astrophysical Journal, 867 (2), [112].
(doi:10.3847/1538-4357/aae5f9).
Abstract
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. 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.
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Published date: 10 November 2018
Additional Information:
Funding Information:
It is a pleasure to thank our long-term collaborators Luis Lehner, Steven L. Liebling, and Carlos Palenzuela, with whom we have had many discussions on adaptive methods for relativistic hydrodynamics. We acknowledge Thomas Sterling, with whom we have discussed the parallel implementation of OAHU. We also thank collaborators Milinda Fernando, Hari Sundar, and Brandon Vernon. This material is based on work supported by the Department of Energy, National Nuclear Security Administration, under award No. DE-NA0002377, the Department of Energy under award No. DE-SC0008809, the National Science Foundation under award Nos. PHY-1308727 and PHY-1607356, and NASA under award No. BL-4363100.
Publisher Copyright:
© 2018. The American Astronomical Society. All rights reserved.
Keywords:
gamma-ray burst: general, hydrodynamics, methods: numerical, relativistic processes
Identifiers
Local EPrints ID: 480937
URI: http://eprints.soton.ac.uk/id/eprint/480937
ISSN: 0004-637X
PURE UUID: 96854dc1-8ff5-44ca-9dab-d23f5a945c91
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Date deposited: 10 Aug 2023 17:00
Last modified: 18 Mar 2024 04:10
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Contributors
Author:
Jackson Debuhr
Author:
Bo Zhang
Author:
Matthew Anderson
Author:
David Neilsen
Author:
Eric W. Hirschmann
Author:
Temistocle Grenga
Author:
Samuel Paolucci
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