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Constrained-transport magnetohydrodynamics with adaptive mesh refinement in CHARM

Journal Article · · The Astrophysical Journal. Supplement Series
 [1];  [2]
  1. ETH, Zurich (Switzerland)
  2. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
+ Show Author Affiliations

We present the implementation of a three-dimensional, second-order accurate Godunov-type algorithm for magnetohydrodynamics (MHD) in the adaptive-mesh-refinement (AMR) cosmological code CHARM. The algorithm is based on the full 12-solve spatially unsplit corner-transport-upwind (CTU) scheme. The fluid quantities are cell-centered and are updated using the piecewise-parabolic method (PPM), while the magnetic field variables are face-centered and are evolved through application of the Stokes theorem on cell edges via a constrained-transport (CT) method. The so-called multidimensional MHD source terms required in the predictor step for high-order accuracy are applied in a simplified form which reduces their complexity in three dimensions without loss of accuracy or robustness. The algorithm is implemented on an AMR framework which requires specific synchronization steps across refinement levels. These include face-centered restriction and prolongation operations and a reflux-curl operation, which maintains a solenoidal magnetic field across refinement boundaries. The code is tested against a large suite of test problems, including convergence tests in smooth flows, shock-tube tests, classical two- and three-dimensional MHD tests, a three-dimensional shock-cloud interaction problem, and the formation of a cluster of galaxies in a fully cosmological context. The magnetic field divergence is shown to remain negligible throughout.

Research Organization:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21), Scientific Discovery through Advanced Computing (SciDAC) (SC21.1 )
Grant/Contract Number:
AC02-05CH11231
OSTI ID:
1511331
Alternate ID(s):
OSTI ID: 21560357
OSTI ID: 1050649
Journal Information:
The Astrophysical Journal. Supplement Series, Journal Name: The Astrophysical Journal. Supplement Series Journal Issue: 1 Vol. 195; ISSN 0067-0049
Publisher:
American Astronomical SocietyCopyright Statement
Country of Publication:
United States
Language:
English

References (61)

An Unsplit 3D Upwind Method for Hyperbolic Conservation Laws journal November 1994
A Staggered Mesh Algorithm Using High Order Godunov Fluxes to Ensure Solenoidal Magnetic Fields in Magnetohydrodynamic Simulations journal March 1999
A Solution-Adaptive Upwind Scheme for Ideal Magnetohydrodynamics journal September 1999
The ∇·B=0 Constraint in Shock-Capturing Magnetohydrodynamics Codes journal July 2000
A Cell-Centered Adaptive Projection Method for the Incompressible Euler Equations journal September 2000
Divergence-Free Adaptive Mesh Refinement for Magnetohydrodynamics journal December 2001
Hyperbolic Divergence Cleaning for the MHD Equations journal January 2002
Divergence- and Curl-Preserving Prolongation and Restriction Formulas journal August 2002
Cosmic Ray Astrophysics book January 2002
The Effect of Nonzero ∇ · B on the numerical solution of the magnetohydrodynamic equations journal May 1980
The Piecewise Parabolic Method (PPM) for gas-dynamical simulations journal April 1984
An upwind differencing scheme for the equations of ideal magnetohydrodynamics journal April 1988
Local adaptive mesh refinement for shock hydrodynamics journal May 1989
Multidimensional upwind methods for hyperbolic conservation laws journal March 1990
On Godunov-type methods near low densities journal February 1991
Magnetohydrodynamics book January 1984
COSMOCR: A numerical code for cosmic ray studies in computational cosmology journal November 2001
On the divergence-free condition in Godunov-type schemes for ideal magnetohydrodynamics: the upwind constrained transport method journal March 2004
An unsplit, cell-centered Godunov method for ideal MHD journal March 2005
An unsplit Godunov method for ideal MHD via constrained transport journal May 2005
A multi-state HLL approximate Riemann solver for ideal magnetohydrodynamics journal September 2005
Kinematic dynamos using constrained transport with high order Godunov schemes and adaptive mesh refinement journal October 2006
A modified higher order Godunov’s scheme for stiff source conservative hydrodynamics journal June 2007
Block structured adaptive mesh and time refinement for hybrid, hyperbolic+N-body systems journal November 2007
Glimm–Godunov’s method for cosmic-ray-hydrodynamics journal November 2007
An unsplit Godunov method for ideal MHD via constrained transport in three dimensions journal April 2008
An unsplit staggered mesh scheme for multidimensional magnetohydrodynamics journal March 2009
A second-order unsplit Godunov scheme for cell-centered MHD: The CTU-GLM scheme journal March 2010
A hybrid scheme for gas–dust systems stiffly coupled via viscous drag journal May 2010
Small-scale structure of two-dimensional magnetohydrodynamic turbulence journal January 1979
Strong magnetic fields in normal galaxies at high redshift journal July 2008
A high order Godunov scheme with constrained transport and adaptive mesh refinement for astrophysical magnetohydrodynamics journal September 2006
Cosmological MHD simulation of a cooling flow cluster journal March 2008
Simulation of magnetohydrodynamic flows - A constrained transport method journal September 1988
On the hydrodynamic interaction of shock waves with interstellar clouds. 1: Nonradiative shocks in small clouds journal January 1994
Shock interactions with magnetized interstellar clouds. 1: Steady shocks hitting nonradiative clouds journal September 1994
Interstellar clouds in high-speed, supersonic flows: Two-dimensional simulations journal January 1995
Numerical Magnetohydrodynamics in Astrophysics: Algorithm and Tests for Multidimensional Flow journal October 1995
Hydra: an Adaptive-Mesh Implementation of P 3M-SPH journal October 1995
The Magnetohydrodynamics of Supersonic Gas Clouds: MHD Cosmic Bullets and Wind‐swept Clumps journal December 1996
The Survival of Interstellar Clouds against Kelvin‐Helmholtz Instabilities journal July 1997
Hydrodynamics of Cloud Collisions in Two Dimensions: The Fate of Clouds in a Multiphase Medium journal December 1997
On the Divergence‐free Condition and Conservation Laws in Numerical Simulations for Supersonic Magnetohydrodynamical Flows journal February 1998
A Divergence‐free Upwind Code for Multidimensional Magnetohydrodynamic Flows journal December 1998
Magnetohydrodynamics of Cloud Collisions in a Multiphase Interstellar Medium journal January 1999
On the Exchange of Kinetic and Magnetic Energy between Clouds and the Interstellar Medium journal May 1999
The Santa Barbara Cluster Comparison Project: A Comparison of Cosmological Hydrodynamics Solutions journal November 1999
High‐Order Upwind Schemes for Multidimensional Magnetohydrodynamics journal February 2000
Enhanced Cloud Disruption by Magnetic Field Interaction journal December 1999
Three‐dimensional Magnetohydrodynamic Numerical Simulations of Cloud‐Wind Interactions journal November 2000
A New Radio–X-Ray Probe of Galaxy Cluster Magnetic Fields journal February 2001
Athena: A New Code for Astrophysical MHD journal September 2008
Castro: a new Compressible Astrophysical Solver. i. Hydrodynamics and Self-Gravity journal May 2010
Resistive Magnetic Field Generation at Cosmic dawn journal February 2011
SIMULATING MAGNETOHYDRODYNAMICAL FLOW WITH CONSTRAINED TRANSPORT AND ADAPTIVE MESH REFINEMENT: ALGORITHMS AND TESTS OF THE AstroBEAR CODE journal May 2009
An adaptive mesh semi-implicit conservative unsplit method for resistive MHD journal January 2005
Interstellar cloud collisions journal July 1985
Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media journal May 1966
Evidence for Strong Extragalactic Magnetic Fields from Fermi Observations of TeV Blazars journal April 2010
A Higher-Order Godunov Method for Multidimensional Ideal Magnetohydrodynamics journal March 1994
Notes on the Eigensystem of Magnetohydrodynamics journal February 1996

Cited By (10)

Self-similar energetics in large clusters of galaxies journal July 2015
A discontinuous Galerkin method for solving the fluid and magnetohydrodynamic equations in astrophysical simulations journal October 2013
Accurate, meshless methods for magnetohydrodynamics journal November 2015
xtroem-fv: a new code for computational astrophysics based on very high order finite-volume methods – I. Magnetohydrodynamics journal November 2015
A constrained-gradient method to control divergence errors in numerical MHD journal July 2016
A moving mesh unstaggered constrained transport scheme for magnetohydrodynamics journal August 2016
SPMHD simulations of structure formation journal February 2018
WOMBAT: A Scalable and High-performance Astrophysical Magnetohydrodynamics Code journal February 2017
Accurate, Meshless Methods for Magneto-Hydrodynamics text January 2015
Self-similar energetics in large clusters of galaxies text January 2015

Figures / Tables (21)

Fig. 1(p. 7)figure Fig. 1
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Table 2(p. 33)table Table 2
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79 ASTRONOMY AND ASTROPHYSICS