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 · Mon Nov 05 23:00:00 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:: Univ. of Notre Dame, IN (United States); Indiana Univ., Bloomington, IN (United States)

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

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

References (53)

Wavelet-based adaptive multiresolution computation of viscous reactive flows Rastigejev, Yevgenii A.; Paolucci, Samuel International Journal for Numerical Methods in Fluids, Vol. 52, Issue 7 https://doi.org/10.1002/fld.1202	journal	January 2006
A Wavelet Collocation Method for the Numerical Solution of Partial Differential Equations Bertoluzza, S.; Naldi, G. Applied and Computational Harmonic Analysis, Vol. 3, Issue 1 https://doi.org/10.1006/acha.1996.0001	journal	January 1996
A Multiresolution Strategy for Reduction of Elliptic PDEs and Eigenvalue Problems Beylkin, Gregory; Coult, Nicholas Applied and Computational Harmonic Analysis, Vol. 5, Issue 2 https://doi.org/10.1006/acha.1997.0226	journal	April 1998
Wavelets and the Numerical Solution of Partial Differential Equations Qian, Sam; Weiss, John Journal of Computational Physics, Vol. 106, Issue 1 https://doi.org/10.1006/jcph.1993.1100	journal	May 1993
A Multilevel Wavelet Collocation Method for Solving Partial Differential Equations in a Finite Domain Vasilyev, Oleg V.; Paolucci, Samuel; Sen, Mihir Journal of Computational Physics, Vol. 120, Issue 1 https://doi.org/10.1006/jcph.1995.1147	journal	August 1995
A Dynamically Adaptive Multilevel Wavelet Collocation Method for Solving Partial Differential Equations in a Finite Domain Vasilyev, Oleg V.; Paolucci, Samuel Journal of Computational Physics, Vol. 125, Issue 2 https://doi.org/10.1006/jcph.1996.0111	journal	May 1996
Accurate Monotonicity-Preserving Schemes with Runge–Kutta Time Stepping Suresh, A.; Huynh, H. T. Journal of Computational Physics, Vol. 136, Issue 1 https://doi.org/10.1006/jcph.1997.5745	journal	September 1997
A Fast Adaptive Wavelet Collocation Algorithm for Multidimensional PDEs Vasilyev, Oleg V.; Paolucci, Samuel Journal of Computational Physics, Vol. 138, Issue 1 https://doi.org/10.1006/jcph.1997.5814	journal	November 1997
Convex ENO High Order Multi-dimensional Schemes without Field by Field Decomposition or Staggered Grids Liu, Xu-Dong; Osher, Stanley Journal of Computational Physics, Vol. 142, Issue 2 https://doi.org/10.1006/jcph.1998.5937	journal	May 1998
Second-Generation Wavelet Collocation Method for the Solution of Partial Differential Equations Vasilyev, Oleg V.; Bowman, Christopher Journal of Computational Physics, Vol. 165, Issue 2 https://doi.org/10.1006/jcph.2000.6638	journal	December 2000
Adaptive Solution of Partial Differential Equations in Multiwavelet Bases Alpert, B.; Beylkin, G.; Gines, D. Journal of Computational Physics, Vol. 182, Issue 1 https://doi.org/10.1006/jcph.2002.7160	journal	October 2002
Symmetric iterative interpolation processes Deslauriers, Gilles; Dubuc, Serge Constructive Approximation, Vol. 5, Issue 1 https://doi.org/10.1007/BF01889598	journal	December 1989
SPH Methods in the Modelling of Compact Objects Rosswog, Stephan Living Reviews in Computational Astrophysics, Vol. 1, Issue 1 https://doi.org/10.1007/lrca-2015-1	journal	October 2015
Adaptive mesh refinement for hyperbolic partial differential equations Berger, Marsha J.; Oliger, Joseph Journal of Computational Physics, Vol. 53, Issue 3 https://doi.org/10.1016/0021-9991(84)90073-1	journal	March 1984
The Piecewise Parabolic Method (PPM) for gas-dynamical simulations Colella, Phillip; Woodward, Paul R. Journal of Computational Physics, Vol. 54, Issue 1 https://doi.org/10.1016/0021-9991(84)90143-8	journal	April 1984
Simultaneous space–time adaptive wavelet solution of nonlinear parabolic differential equations Alam, Jahrul M.; Kevlahan, Nicholas K. -R.; Vasilyev, Oleg V. Journal of Computational Physics, Vol. 214, Issue 2 https://doi.org/10.1016/j.jcp.2005.10.009	journal	May 2006
Conservative, special-relativistic smoothed particle hydrodynamics Rosswog, Stephan Journal of Computational Physics, Vol. 229, Issue 22 https://doi.org/10.1016/j.jcp.2010.08.002	journal	November 2010
WAMR: An adaptive wavelet method for the simulation of compressible reacting flow. Part I. Accuracy and efficiency of algorithm Paolucci, Samuel; Zikoski, Zachary J.; Wirasaet, Damrongsak Journal of Computational Physics, Vol. 272 https://doi.org/10.1016/j.jcp.2014.01.025	journal	September 2014
WAMR: An adaptive wavelet method for the simulation of compressible reacting flow. Part II. The parallel algorithm Paolucci, Samuel; Zikoski, Zachary J.; Grenga, Temistocle Journal of Computational Physics, Vol. 272 https://doi.org/10.1016/j.jcp.2014.03.059	journal	September 2014
Astrophysical smooth particle hydrodynamics Rosswog, Stephan New Astronomy Reviews, Vol. 53, Issue 4-6 https://doi.org/10.1016/j.newar.2009.08.007	journal	April 2009
A numerical approach for solving singular nonlinear Lane–Emden type equations arising in astrophysics Kazemi Nasab, A.; Kılıçman, A.; Pashazadeh Atabakan, Z. New Astronomy, Vol. 34 https://doi.org/10.1016/j.newast.2014.06.008	journal	January 2015
THC: a new high-order finite-difference high-resolution shock-capturing code for special-relativistic hydrodynamics Radice, D.; Rezzolla, L. Astronomy & Astrophysics, Vol. 547 https://doi.org/10.1051/0004-6361/201219735	journal	October 2012
Wavelet-based decomposition and analysis of structural patterns in astronomical images Mertens, Florent; Lobanov, Andrei Astronomy & Astrophysics, Vol. 574 https://doi.org/10.1051/0004-6361/201424566	journal	January 2015
An efficient shock-capturing central-type scheme for multidimensional relativistic flows: I. Hydrodynamics Del Zanna, L.; Bucciantini, N. Astronomy & Astrophysics, Vol. 390, Issue 3 https://doi.org/10.1051/0004-6361:20020776	journal	August 2002
Assessment of a high-resolution central scheme for the solution of the relativistic hydrodynamics equations Lucas-Serrano, A.; Font, J. A.; Ibáñez, J. M. Astronomy & Astrophysics, Vol. 428, Issue 2 https://doi.org/10.1051/0004-6361:20035731	journal	November 2004
Relativistic Rayleigh–Taylor instability of a decelerating shell and its implications for gamma-ray bursts Levinson, Amir Geophysical & Astrophysical Fluid Dynamics, Vol. 104, Issue 1 https://doi.org/10.1080/03091920903479742	journal	February 2010
An adaptive wavelet-collocation method for shock computations Regele, J. D.; Vasilyev, O. V. International Journal of Computational Fluid Dynamics, Vol. 23, Issue 7 https://doi.org/10.1080/10618560903117105	journal	August 2009
Primitive Variable Solvers for Conservative General Relativistic Magnetohydrodynamics Noble, Scott C.; Gammie, Charles F.; McKinney, Jonathan C. The Astrophysical Journal, Vol. 641, Issue 1 https://doi.org/10.1086/500349	journal	April 2006
RAM: A Relativistic Adaptive Mesh Refinement Hydrodynamics Code Zhang, Weiqun; MacFadyen, Andrew I. The Astrophysical Journal Supplement Series, Vol. 164, Issue 1 https://doi.org/10.1086/500792	journal	May 2006
Convective Instability of a Relativistic Ejecta Decelerated by a Surrounding Medium: an Origin of Magnetic Fields in Gamma-Ray Bursts? Levinson, Amir The Astrophysical Journal, Vol. 705, Issue 2 https://doi.org/10.1088/0004-637X/705/2/L213	journal	October 2009
Rayleigh-Taylor Instability in a Relativistic Fireball on a Moving Computational grid Duffell, Paul C.; MacFadyen, Andrew I. The Astrophysical Journal, Vol. 775, Issue 2 https://doi.org/10.1088/0004-637X/775/2/87	journal	September 2013
A Second-Order Godunov Method for Multi-Dimensional Relativistic Magnetohydrodynamics Beckwith, Kris; Stone, James M. The Astrophysical Journal Supplement Series, Vol. 193, Issue 1 https://doi.org/10.1088/0067-0049/193/1/6	journal	January 2011
Tess: a Relativistic Hydrodynamics code on a Moving Voronoi mesh Duffell, Paul C.; MacFadyen, Andrew I. The Astrophysical Journal Supplement Series, Vol. 197, Issue 2 https://doi.org/10.1088/0067-0049/197/2/15	journal	November 2011
Cafe: a new Relativistic mhd code Lora-Clavijo, F. D.; Cruz-Osorio, A.; Guzmán, F. S. The Astrophysical Journal Supplement Series, Vol. 218, Issue 2 https://doi.org/10.1088/0067-0049/218/2/24	journal	June 2015
Relativistic MHD with adaptive mesh refinement Anderson, Matthew; Hirschmann, Eric W.; Liebling, Steven L. Classical and Quantum Gravity, Vol. 23, Issue 22 https://doi.org/10.1088/0264-9381/23/22/025	journal	October 2006
GRHydro: a new open-source general-relativistic magnetohydrodynamics code for the Einstein toolkit Mösta, Philipp; Mundim, Bruno C.; Faber, Joshua A. Classical and Quantum Gravity, Vol. 31, Issue 1 https://doi.org/10.1088/0264-9381/31/1/015005	journal	November 2013
Classification methods for noise transients in advanced gravitational-wave detectors Powell, Jade; Trifirò, Daniele; Cuoco, Elena Classical and Quantum Gravity, Vol. 32, Issue 21 https://doi.org/10.1088/0264-9381/32/21/215012	journal	October 2015
Shock Corrugation by Rayleigh-Taylor Instability in Gamma-Ray Burst Afterglow jets Duffell, Paul C.; MacFadyen, Andrew I. The Astrophysical Journal, Vol. 791, Issue 1 https://doi.org/10.1088/2041-8205/791/1/L1	journal	July 2014
Non-parametric transient classification using adaptive wavelets Varughese, Melvin M.; von Sachs, Rainer; Stephanou, Michael Monthly Notices of the Royal Astronomical Society, Vol. 453, Issue 3 https://doi.org/10.1093/mnras/stv1816	journal	September 2015
A new class of accurate, mesh-free hydrodynamic simulation methods Hopkins, Philip F. Monthly Notices of the Royal Astronomical Society, Vol. 450, Issue 1 https://doi.org/10.1093/mnras/stv195	journal	April 2015
Accurate, meshless methods for magnetohydrodynamics Hopkins, Philip F.; Raives, Matthias J. Monthly Notices of the Royal Astronomical Society, Vol. 455, Issue 1 https://doi.org/10.1093/mnras/stv2180	journal	November 2015
Excitation of magnetohydrodynamic modes with gravitational waves: A testbed for numerical codes Duez, Matthew D.; Liu, Yuk Tung; Shapiro, Stuart L. Physical Review D, Vol. 72, Issue 2 https://doi.org/10.1103/PhysRevD.72.024029	journal	July 2005
General relativistic simulations of black-hole–neutron-star mergers: Effects of magnetic fields Etienne, Zachariah B.; Liu, Yuk Tung; Paschalidis, Vasileios Physical Review D, Vol. 85, Issue 6 https://doi.org/10.1103/PhysRevD.85.064029	journal	March 2012
Multiresolution representations using the autocorrelation functions of compactly supported wavelets Saito, N.; Beylkin, G. IEEE Transactions on Signal Processing, Vol. 41, Issue 12 https://doi.org/10.1109/78.258102	journal	January 1993
E pur si muove: Galilean-invariant cosmological hydrodynamical simulations on a moving mesh Springel, Volker Monthly Notices of the Royal Astronomical Society, Vol. 401, Issue 2 https://doi.org/10.1111/j.1365-2966.2009.15715.x	journal	January 2010
On Godunov-Type Methods for Gas Dynamics Einfeldt, Bernd SIAM Journal on Numerical Analysis, Vol. 25, Issue 2 https://doi.org/10.1137/0725021	journal	April 1988
On the Representation of Operators in Bases of Compactly Supported Wavelets Beylkin, G. SIAM Journal on Numerical Analysis, Vol. 29, Issue 6 https://doi.org/10.1137/0729097	journal	December 1992
Wavelet-Like Bases for the Fast Solution of Second-Kind Integral Equations Alpert, B.; Beylkin, G.; Coifman, R. SIAM Journal on Scientific Computing, Vol. 14, Issue 1 https://doi.org/10.1137/0914010	journal	January 1993
Adaptive Wavelet Schemes for Parabolic Problems: Sparse Matrices and Numerical Results Chegini, Nabi; Stevenson, Rob SIAM Journal on Numerical Analysis, Vol. 49, Issue 1 https://doi.org/10.1137/100800555	journal	January 2011
On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws Harten, Amiram; Lax, Peter D.; Leer, Bram van SIAM Review, Vol. 25, Issue 1 https://doi.org/10.1137/1025002	journal	January 1983
Solving Hyperbolic PDEs Using Interpolating Wavelets Holmström, Mats SIAM Journal on Scientific Computing, Vol. 21, Issue 2 https://doi.org/10.1137/S1064827597316278	journal	January 1999
Smoothed Particle Hydrodynamics in Astrophysics Springel, Volker Annual Review of Astronomy and Astrophysics, Vol. 48, Issue 1 https://doi.org/10.1146/annurev-astro-081309-130914	journal	August 2010
Disco: a 3d Moving-Mesh Magnetohydrodynamics code Designed for the Study of Astrophysical Disks Duffell, Paul C. The Astrophysical Journal Supplement Series, Vol. 226, Issue 1 https://doi.org/10.3847/0067-0049/226/1/2	journal	August 2016

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