My MHD equations thus far PDF

    Hydrodynamic References:

  • A Numerical Study of Relativistic Fluid Collapse (Scott Noble's Ph.D. Thesis)
  • Computational Ultrarelativistic Hydrodynamics (Ian Hawke's Ph.D. Thesis)
  • Extremely Relativistic Fluids in Strong-Field Gravity (David Neilsen's Ph.D. Thesis)
  • 3D Relativistic Hydrodynamics Miguel Aloy's Thesis
  • Numerical Hydrodynamics in Special Relativity Martí and Müller
  • Numerical Relativistic Hydrodynamics: A Local Characteristic Approach Martí
  • Numerical 3+1 GR Hydrodynamics: A Local Characteristic Approach Banyuls

    • Magnetohydrodynamics:

  • Primitive Variable Solvers for Conservative General Relativistic Magnetohydrodynamics Gammie, Noble, McKinney, Del Zanna
  • An HLLC Riemann solver for relativistic flows ­ II. MHD Mignone Bodo This contains a really good primitive variable solver
  • A Shock Capturing Scheme for Relativistic Flows Del Zanna
  • Self-Gravitational MHD with Adaptive Mesh Refinement for Protostellar Collapse Matsumoto
  • Two-component MHD outflows around young stellar objects Meliani Newtonian-viscous MHD

    Magnetic Field Treatments:

  • Constraint Preserving Transport for Magnetohydrodynamics Frontiers in Numerical Relativity, 179, 1989 NASAADS
  • HARM: A NUMERICAL SCHEME FOR GENERAL RELATIVISTIC MAGNETOHYDRODYNAMICS (arXiv) This offers a simple explanation of Toth's magnetic field treatment (see below)
  • An Approximate Riemann Solver for MHD Powell's Paper
  • The ∇⋅B=0 Constrain In Shock-Capturing MHD Codes Gabor Töth
  • Constrained Transport Algorithms for Numerical Relativity. I. Development of a Finite Difference Scheme Meier

  • Hyperbolic Divergence Cleaning for the MHD Equations J. Comp. Phys 175, 645

    Specific Problems:

    Configuration Tests:

  • A Numerical Study of Nonspherical Black Hole Accretion I Hawley Etal.
  • A Numerical Study of Nonspherical Black Hole Accretion II Hawley Etal.

    Bondi-Holye Accretion:

    Note: There are far too many papers on this topic to form an entire list on this webpage.

    Relativistic:

  • Accretion of Matter by Condensed Objects Michel
  • Numerical simulations of relativistic wind accretion on to black holes using Godunov-type methods astro-ph/9910433v1
  • Non-axisymmetric relativistic Bondi-Hoyle accretion onto a Schwarzschild black hole MNRAS 298,835
  • Numerical Study of Relativistic Bondi-Hoyle Accretion onto a Moving Black Hole: Axisymmetric Computations in a Schwarzschild Background ApJ 494,297
  • Non-axisymmetric relativistic Bondi-Hoyle accretion on to a Kerr black hole MNRAS 305,920
  • Relativistic Hydrodynamics Around Black Holes and Horizon Adapted Coordinate Systems (Phys Rev D 98)
  • A 'Horizon-adapted' Approach to the Study of Relativistic Accretion Flows onto Rotating Black Holes ApJ 507, L67
  • A review of Bondi-Hoyle-Lyttleton accretion Elsevier
  • Accretion powered spherical wind in general relativity Astro. Astrophys. 376, 697
  • Fluid accretion onto a spherical black hole: Relativistic description versus the Bondi model arXiv:gr-qc/9907028
  • Relativistic Accretion arXiv:astro-ph/9902001
  • Maximum Accretion Efficiency in General Theory of Relativity arXiv:astro-ph/9811402

  • Newtonian:

  • On the mechanism of accretion by stars MNRAS 104, 273
  • On Spherically Symmetric Accretion MNRAS 112,195
  • The Unsteady Accretion Problem MNRAS 112,374
  • A new solution to the accretion problem MNRAS 160, 255
  • An investigation of the stability of the Bondi-Hoyle model of accretion flow MNRAS 180, 491
  • An analytic study of Bondi-Hoyle-Lyttleton accretion I. Stationary Flows Astrophys. 1996
  • An analytic study of Bondi-Hoyle-Lyttleton accretion II. Local Stability Analysis Astron Astrophys. 347 901
  • Hoyle-Lyttleton Accretion on Accretion DisksAstron. Soc. Japan 51,151
  • A fresh look at the unstable simulations of Bondi-Hoyle-Lyttleton accretion A&A 435, 397
  • Wind accretion by a binary stellar system and disc formation MNRAS 350, 1366
  • Bondi Accretion in the Presence of Vorticity ApJ 618,757
  • On spherically symmetrical accretion in fractal media MNRAS 378,L34
  • Three-dimensional hydrodynamic Bondi-Hoyle accretion. 1: Code validation and stationary accretors ApJ 427, 342
  • Three-dimensional hydrodynamic Bondi-Hoyle accretion. 2: Homogeneous medium at Mach 3 with gamma = 5/3 ApJ 427,351
  • Three-dimensional hydrodynamic Bondi-Hoyle accretion III. Mach 0.6, 1.4 and 10; gamma=5/3 Astron. Astrophys. Suppl 106,505
  • Three-dimensional hydrodynamic Bondi-Hoyle accretion IV. Specific heat ratio 4/3 Astron. Astrophys. Suppl. 113,133
  • Three-dimensional hydrodynamic Bondi-Hoyle accretion V. Specific heat ratio 1.01, nearly isothermal flow Astrophys. 1995
  • "Tail-End" Bondi-Hoyle Accretion in Young Star Clusters: Implications for Disks, Planets, and Stars ApJ, 135,2380
  • On the 'flip-flop' instability of Bondi-Hoyle accretion flows MNRAS 253, 633
  • The Physics of Wind-Fed Accretion arXiv:0806.1073
  • Accretion research: how it started The Observatory, 107, 245

    Schwarzschild Steady State Accretion:

  • Accretion of Matter by Condensed Objects Michel
  • A numerical study of nonspherical black hole accretion. I - Equations and Test ProblemsApJ. 277, 269
  • A numerical study of nonspherical black hole accretion. II - Finite differencing and code calibration ApJ Supp. 55, 211

    Kerr Steady State Accretion:

  • Efficiency of Magnetized Thin Accretion Disks In The Kerr Metric ApJ 522 L57

    Kerr Accretion:

  • Hydrodynamic Simulations of Tilted Thick-Disk Accretion onto a Kerr Black Hole ApJ 623, 347
  • Force-Free Magnetosphere of an Accreting Kerr Black Hole arXiv:astro-ph/0503518
  • Force-Free Magnetosphere of an Accretion Disk-Black Hole System. II. Kerr Geometry ApJ 620, 889
  • Magnetically Driven Accretion in the Kerr Metric. III. Unbound Outflows ApJ 620, 878
  • Charged matter accretion on Kerr black holes.
  • Magnetically Driven Accretion Flows in the Kerr Metric. I. Models and Overall Structure ApJ 599, 1238
  • Magnetohydrodynamic Shock Conditions for Accreting Plasma onto Kerr Black Holes. I. ApJ 572, 950
  • Simulation of Jet Formation from Magnetized Accretion Disk Around Kerr Black Hole
  • Efficiency of Magnetized Thin Accretion Disks in the Kerr Metric ApJ 522, L57
  • Advection-dominated Accretion Flows in the Kerr Metric. II. Steady State Global Solutions ApJ 504, 419
  • Advection-dominated Accretion Flows in the Kerr Metric. I. Basic Equations ApJ 498, 313
  • The oscillatory shape of the stationary twisted disc around a Kerr black hole MNRAS 285, 394
  • Hydrodynamic accretion on to a rapidly rotating Kerr black hole MNRAS 283, 1264
  • Optically thin accretion disks in the Kerr metric ApJ 441, 765

  • Jets and Other Accretion Phenomenon:

  • General Relativistic Magnetohydrodynamic Simulations of Jet Formation and Large-Scale Propagation from Black Hole Accretion Systems astro-ph/0603045
  • Accretion onto Black Holes Living Reviews in Relativity
  • An analytic study of Bondi-Hoyle-Lyttleton accretion Astrophys,347,901

    • Shocks:

  • Particle acceleration and relativistic shocks astro-ph/9905069

    • Full General Relativity Treatments and Tests:

  • Magnetohydrodynamics in full general relativity: Formulation and tests (astro-ph/0507383)
  • Collapse and black hole formation in magnetized, differentially rotating neutron stars (gr-qc/0610103)
  • TOTAL VARIATION DIMINISHING SCHEME FOR RELATIVISTIC MAGNETOHYDRODYNAMICS Balsara's Paper
  • Robustness of a high-resolution central scheme for hydrodynamic simulations in full general relativity (gr-qc/0507099)
  • A Numerical Method For General Relativistic MHD ApJ, 589, 458
  • Relativistic MHD in Dynamical Spacetimes: Numerical Methods and Tests Duez
  • Numerical 3+1 GRMHD: A Local Characteristic Approach Antón Great GRMHD tests
  • GR MHD for the Numerical Construction of Dynamical Spacetimes ApJ 585 921
  • An implicit numerical algorithm for solving the general relativistic hydrodynamical equations around accreting compact objects Hujeirat
  • A new Godunov-type numerical code with a non-linear Riemann solver for equations of relativistic hydrodynamics Tytarenko (It really looks like all the other solvers)

    Rotation Specifically:

  • Black Hole Astrophysics: Magnetohydrodynamics on the Kerr Geometry Mueller's Thesis
  • Spin, Accretion and the Cosmological Growth of Supermassive Black Holes (astro-ph/0411156)

    • Jets:

  • GR MHD Simulations of the Jet Formation and Large-scale Propagation from BH Accretion Systems McKinney
  • General relativistic MHD simulations of black hole accretion disks and jets Hawley etal.
  • Relativistic fluid disks in orbit around Kerr black holes Fishbone etal.

    • Field Theory Approach:

  • Perfect magnetohydrodynamics as a field theory Bekenstein

    • Adaptive Mesh Refinement:

  • Relativistic MHD with adaptive mesh refinement Class. Quant. Grav. 23,6503
  • COSMOS++: Relativistic MHD on Unstructured Grids With Local Adaptive Refinement ApJ 635, 723
  • Adaptive Mesh Refinement for Hyperbolic PDE's Berger, Oliger
  • Local Adaptive Mesh Refinement for Shock Hydrodynamics Berger, Colella
  • Adaptive Mesh Refinement using Wave-Propagation Algorithms for Hyperbolic Systems Berger, LeVeque
  • Three-Dimensional Adaptive Mesh Refinement for Hyperbolic Conservation Laws Bell, Berger, etal.
  • AMR for Coupled Elliptic-Hyperbolic Systems Pretorius, Choptuik

  • Elliptic PDE Solution Techniques (Not Multigrid) Berkley

    • Relevant Living Review Articles (Relevant directly to this research)

  • Initial Data for Numerical Relativity Cook
  • Rotating Stars in Relativity Stergioulas
  • Numerical Hydrodynamics in Special Relativity Marti etal
  • Numerical Magnetohydrodynamics in General Relativity Font

    • Mixing Fluids (List offered by Dr. Ian Hawke of Southampton University)

  • A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows Fredkiw
  • A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles Sussman
  • A Coupled Level Set and Volume-of-Fluid Method for Computing 3D and Axisymmetric Incompressible Two-Phase Flows Sussman
  • LEVEL SET METHODS FOR FLUID INTERFACES Sethian
  • DIFFUSE-INTERFACE METHODS IN FLUID MECHANICS Anderson
  • DIRECT NUMERICAL SIMULATION OF FREE-SURFACE AND INTERFACIAL FLOW Scardovelli
  • THE EXPLICIT SIMPLIFIED INTERFACE METHOD FOR COMPRESSIBLE MULTICOMPONENT FLOWS Lombard

    More Fluid Mixing
  • An Efficient Shock-Capturing Algorithm for Compressible Multicomponent Problems Shyue
  • A Runge-Kutta Discontinuous-Galerkin Level-Set Method For Unsteady Compressible Two-Fluid Flow Naber
  • A Fully Conservative Model for Two-Fluid Flow Whackers
  • Numerical Solver for Compressible Two-Fluid Flow Naber
  • Five-Equation Model for Compressible Two-Fluid Flow Whackers
  • Improved Capturing of Contact Discontinuities for Two-Fluid Flows Duivesteijn

    • Instabilities

  • Magnetorotational Instability in the Kerr Metric Charles Gammie
  • Hydrodynamic Instability of a Slim Disk in a Stationary GeometryAraya-Góchez
  • Instability, turbulence, and enhanced transport in accretion disks Balbus Hawley

    Spectral Methods

  • A Fast Stroboscopic Spectral Method for Rotating Systems in Numerical Relativity Bonazzola etal

    • Smoothed Particle Hydrodynamics

  • SPH Northwestern Manual
  • 3-D Numerical Simulations of Rotating Jets (astro-ph/0409285)
  • Hydrodynamic Flow past a Cylinder Brian Schlatter's Thesis
  • A Parallel Implementation of a Fluid Flow Simulation Using Smoothed Particle Hydrodynamics Keith Vertanen
  • Magnetic Fields in Astrophysics Daniel J. Price
  • Smoothed Particle MHD - I Algorithm and tests in 1D DJ Price & JJ Monaghan
  • Smoothed Particle MHD - II Variational Principles and Variable Smoothing-length terms DJ Price & JJ Monaghan
  • Smoothed Particle MHD - III Multidimensional tests DJ Price & JJ Monaghan
  • A Numerical Approach to the Testing of the Fission Hypothesis L.B. Lucy

  • A comparison between SPH and PPM: simulations of stellar collisions A&A 272, 430

    Viscid MHD

  • A constrained-transp ort magnetohydro dynamics algorithm with near-spectral resolution. arXiv:0709.1234

    • Older papers, which lead to astrophysical results

  • Robustness of a high-resolution central scheme for hydrodynamic simulations in full general relativity (gr-qc/0507099)
  • The Supercritical Accretion Disk in SS 433 and Ultraluminous X-ray sources(gr-qc/0507099)

    • Newtonian Hydrodynamics

  • The Method of Transport for Mixed Hyperbolic-parabolic Systems (Parabolic Finite Volume)
  • Conservation of circulation in MHD Bekenstein, Oron
  • Robust Euler MHD Equations Newtonian MHD

    • Quite a Valuable reference list

  • Toth's Puplications

    • Other Papers of Interest

  • Numerical Methods and PDE quick tutorial

  • Katherine Blundell's Publications Page

  • A Summary of Numerical Methods for Time-Depenednant Advection-Dominated PDEs

  • SS433

  • SS433 in ApJ

  • Accretions Disks in ApJ

  • Introduction to (dis)continuous Galerkin FEM

    • A little history for CFD

  • Computational Fluid Dynamics: Science and Tool

    • Lectures on Different Topics

  • Accretion

    • Books

    An Introduction to Magnetohydrodynamics, P.A. Davidson, Cambridge Texts

    This Website Maintained by ajpenner@physics.ubc.ca. Supported by Matt Choptuik