refs.bib

@ARTICLE{almgren:2010,
   author = {{Almgren}, A.~S. and {Beckner}, V.~E. and {Bell}, J.~B. and 
{Day}, M.~S. and {Howell}, L.~H. and {Joggerst}, C.~C. and {Lijewski}, M.~J. and 
{Nonaka}, A. and {Singer}, M. and {Zingale}, M.},
    title = "{CASTRO: A New Compressible Astrophysical Solver. I. Hydrodynamics and Self-gravity}",
  journal = {Astrophys J},
archivePrefix = "arXiv",
   eprint = {1005.0114},
 primaryClass = "astro-ph.IM",
 keywords = {equation of state, gravitation, hydrodynamics, methods: numerical, nuclear reactions, nucleosynthesis, abundances},
     year = 2010,
    month = jun,
   volume = 715,
    pages = {1221-1238},
      doi = {10.1088/0004-637X/715/2/1221},
   adsurl = {http://adsabs.harvard.edu/abs/2010ApJ...715.1221A},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@ARTICLE{colella:1990,
   author = {{Colella}, P.},
    title = "{Multidimensional upwind methods for hyperbolic conservation laws}",
  journal = {Journal of Computational Physics},
 keywords = {ADVECTION, BOUNDARY VALUE PROBLEMS, COMPUTATIONAL GRIDS, CONSERVATION LAWS, FINITE DIFFERENCE THEORY, HYPERBOLIC FUNCTIONS, ALGORITHMS, CAUCHY PROBLEM, PREDICTOR-CORRECTOR METHODS},
     year = 1990,
    month = mar,
   volume = 87,
    pages = {171-200},
      doi = {10.1016/0021-9991(90)90233-Q},
   adsurl = {http://adsabs.harvard.edu/abs/1990JCoPh..87..171C},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}


@ARTICLE{colella:1985,
   author = {{Colella}, P.},
    title = "{A direct Eulerian MUSCL scheme for gas dynamics}",
  journal = {SIAM J Sci Stat Comput},
     year = 1985,
   volume = 6,
  number = 1,
    pages = {104-117}
}


@ARTICLE{colellaglaz:1985,
   author = {{Colella}, P. and {Glaz}, H.~M.},
    title = "{Efficient solution algorithms for the Riemann problem for real gases}",
  journal = {Journal of Computational Physics},
 keywords = {CAUCHY PROBLEM, COMPRESSIBLE FLOW, EQUATIONS OF STATE, GAS DYNAMICS, INVISCID FLOW, POLYTROPIC PROCESSES, ALGORITHMS, BOUNDARY VALUE PROBLEMS, CARTESIAN COORDINATES, FINITE DIFFERENCE THEORY, JACOBI MATRIX METHOD, RANKINE-HUGONIOT RELATION, SHOCK TUBES, SHOCK WAVES},
     year = 1985,
    month = jun,
   volume = 59,
    pages = {264-289},
      doi = {10.1016/0021-9991(85)90146-9},
   adsurl = {http://adsabs.harvard.edu/abs/1985JCoPh..59..264C},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}


@ARTICLE{colellawoodward:1984,
   author = {{Colella}, P. and {Woodward}, P.~R.},
    title = "{The Piecewise Parabolic Method (PPM) for Gas-Dynamical Simulations}",
  journal = {Journal of Computational Physics},
     year = 1984,
    month = sep,
   volume = 54,
    pages = {174-201},
      doi = {10.1016/0021-9991(84)90143-8},
   adsurl = {http://adsabs.harvard.edu/abs/1984JCoPh..54..174C},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}


@ARTICLE{millercolella:2002,
   author = {{Miller}, G.~H. and {Colella}, P.},
    title = "{A Conservative Three-Dimensional Eulerian Method for Coupled Solid-Fluid Shock Capturing}",
  journal = {Journal of Computational Physics},
     year = 2002,
    month = nov,
   volume = 183,
    pages = {26-82},
      doi = {10.1006/jcph.2002.7158},
   adsurl = {http://adsabs.harvard.edu/abs/2002JCoPh.183...26M},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}


@ARTICLE{saltzman:1994,
   author = {{Saltzman}, J.},
    title = "{An Unsplit 3D Upwind Method for Hyperbolic Conservation Laws}",
  journal = {Journal of Computational Physics},
     year = 1994,
    month = nov,
   volume = 115,
    pages = {153-168},
      doi = {10.1006/jcph.1994.1184},
   adsurl = {http://adsabs.harvard.edu/abs/1994JCoPh.115..153S},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}


@Book{toro:1997,
  author =       {E. F. Toro},
  title =        {Riemann Solvers and Numerical Methods for Fluid Dynamics},
  publisher =    {Springer},
  year =         {1997},
}

@book{leveque:2002,
  author = {Randall J. LeVeque},
  publisher = {Cambridge University Press },
  title = {Finite-Volume Methods for Hyperbolic Problems},
  year = 2002
}


@ARTICLE{plewamuller:1999,
   author = {{Plewa}, T. and {M{\"u}ller}, E.},
    title = "{The consistent multi-fluid advection method}",
  journal = {Astron Astrophys},
   eprint = {arXiv:astro-ph/9807241},
 keywords = {HYDRODYNAMICS, NUCLEAR REACTIONS, NUCLEOSYNTHESIS, ABUNDANCES, METHODS: NUMERICAL, STARS: SUPERNOVAE: GENERAL},
     year = 1999,
    month = feb,
   volume = 342,
    pages = {179-191},
   adsurl = {http://adsabs.harvard.edu/abs/1999A%26A...342..179P},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@ARTICLE{bryan:1995,
   author = {{Bryan}, G.~L. and {Norman}, M.~L. and {Stone}, J.~M. and {Cen}, R. and 
{Ostriker}, J.~P.},
    title = "{A piecewise parabolic method for cosmological hydrodynamics}",
  journal = {Computer Physics Communications},
     year = 1995,
    month = aug,
   volume = 89,
    pages = {149-168},
      doi = {10.1016/0010-4655(94)00191-4},
   adsurl = {http://adsabs.harvard.edu/abs/1995CoPhC..89..149B},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}


@book{multigridtutorial,
  author = {Briggs, W.~L. and Henson, V-E. and McCormick, S.~F.},
  publisher = {SIAM},
  title = {A Mutigrid Tutorial, 2nd Ed.},
  year = 2000
}


@book{colellanotes,
  author = {Colella, P. and Puckett, E.~G.},
  publisher = {unpublished manuscript},
  title = {Modern Numerical Methods for Fluid Flow},
  note = {obtained from http://www.amath.unc.edu/Faculty/minion/class/puckett/}
}

@ARTICLE{BCG,
   author = {{Bell}, J.~B. and {Colella}, P. and {Glaz}, H.~M.},
    title = "{A Second Order Projection Method for the Incompressible Navier-Stokes Equations}",
  journal = {Journal of Computational Physics},
     year = 1989,
    month = dec,
   volume = 85,
    pages = {257},
      doi = {10.1016/0021-9991(89)90151-4},
   adsurl = {http://adsabs.harvard.edu/abs/1989JCoPh..85..257B},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}


@INPROCEEDINGS{BCH,
        AUTHOR = {J. B. Bell and P. Colella and L. H. Howell},
        TITLE = {An efficient second-order projection method
         for viscous incompressible flow},
        YEAR = {1991},
        BOOKTITLE = {Proceedings of the Tenth AIAA Computational
                     Fluid Dynamics Conference},
        MONTH = Jun,
        ORGANIZATION = {AIAA},
        PAGES = {360--367},
        note = {see also: https://seesar.lbl.gov/anag/publications/colella/A\_2\_10.pdf}
}

@ARTICLE{ABS,
        TITLE = {A numerical method for the incompressible {N}avier-{S}tokes
        equations based on an approximate projection},
        AUTHOR = {A. S. Almgren and J. B. Bell and W. G. Szymczak},
        YEAR = {1996},
        VOLUME = {17},
        NUMBER = {2},
        MONTH = Mar,
        JOURNAL = {SIAM J. Sci. Comput.},
        PAGES = {358--369}
}

@ARTICLE{chorin:1968,
        AUTHOR = {A. J. Chorin},
        TITLE = {Numerical Solution of the {N}avier-{S}tokes Equations},
        JOURNAL = {Math. Comp.},
        VOLUME = {22},
        PAGES = {745--762},
        YEAR = {1968}
}

@ARTICLE{MartinColella,
   author = {{Martin}, D.~F. and {Colella}, P.},
    title = "{A Cell-Centered Adaptive Projection Method for the Incompressible Euler Equations}",
  journal = {Journal of Computational Physics},
     year = 2000,
    month = sep,
   volume = 163,
    pages = {271-312},
      doi = {10.1006/jcph.2000.6575},
   adsurl = {http://adsabs.harvard.edu/abs/2000JCoPh.163..271M},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@TECHREPORT{rider,
    author = {{Rider}, W.~J. },
    title = {Approximate Projection Methods for Incompressible Flow: Implementation, Variants and Robustness.},
    institution = {LANL UNCLASSIFIED REPORT LA-UR-94-2000, LOS ALAMOS NATIONAL LABORATORY},
    year = {1995}
}


@ARTICLE{ABC,
author =   {A. S. Almgren and J. B. Bell and W. Y. Crutchfield},
title =    {Approximate Projection Methods: Part {I}. {I}nviscid Analysis},
journal =  {SIAM J. Sci. Comput.},
volume={22},
number={4},
pages={1139--59},
year =     {2000}
}


@article{BellMarcus,
title = "A second-order projection method for variable-density flows",
journal = "Journal of Computational Physics",
volume = "101",
number = "2",
pages = "334 - 348",
year = "1992",
note = "",
issn = "0021-9991",
doi = "10.1016/0021-9991(92)90011-M",
url = "http://www.sciencedirect.com/science/article/pii/002199919290011M",
author = "Bell, J.~B. and Marcus, D.~L."
}


@Article{SNpaper,
  author  =      {J.~B. Bell and M.~S. Day and C.~A. Rendleman and
                  S.~E. Woosley and M.~A. Zingale},
  title   =      {Adaptive low {M}ach number simulations of nuclear flame microphysics},
  journal =      {Journal of Computational Physics},
  year    =      {2004},
  volume  =      {195},
  number  =      {2},
  pages   =      {677-694}
}

@Article{pember-flame,
  author =       {R. B. Pember and L. H. Howell and J. B. Bell and
                  P. Colella and W. Y. Crutchfield and W. A. Fiveland
                  and J. P. Jessee},
  title =        {An Adaptive Projection Method for Unsteady
                  Low-{M}ach Number Combustion},
  journal =      {Comb. Sci. Tech.},
  volume =       {140},
  pages =        {123--168},
  year =         {1998},
}

@ARTICLE{DayBell:2000,
  author={M. S. Day and J. B. Bell},
  title={Numerical simulation of laminar reacting flows with complex chemistry},
  journal={Combust. Theory Modelling},
  volume={4},
  number={4},
  pages={535-556},
  year={2000}
 }

@ARTICLE{minion:1996,
   author = {{Minion}, M.~L.},
    title = "{A Projection Method for Locally Refined Grids}",
  journal = {Journal of Computational Physics},
     year = 1996,
   volume = 127,
    pages = {158--177}
}

@ARTICLE{malone:2011,
   author = {{Malone}, C.~M. and {Nonaka}, A. and {Almgren}, A.~S. and {Bell}, J.~B. and 
{Zingale}, M.},
    title = "{Multidimensional Modeling of Type I X-ray Bursts. I. Two-dimensional Convection Prior to the Outburst of a Pure $^{4}$He Accretor}",
  journal = {ApJ},
archivePrefix = "arXiv",
   eprint = {1012.0609},
 primaryClass = "astro-ph.HE",
 keywords = {convection, hydrodynamics, methods: numerical, stars: neutron, X-rays: bursts},
     year = 2011,
    month = feb,
   volume = 728,
      eid = {118},
    pages = {118},
      doi = {10.1088/0004-637X/728/2/118},
   adsurl = {http://adsabs.harvard.edu/abs/2011ApJ...728..118M},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@ARTICLE{hse,
   author = {{Zingale}, M. and {Dursi}, L.~J. and {ZuHone}, J. and {Calder}, A.~C. and 
{Fryxell}, B. and {Plewa}, T. and {Truran}, J.~W. and {Caceres}, A. and 
{Olson}, K. and {Ricker}, P.~M. and {Riley}, K. and {Rosner}, R. and 
{Siegel}, A. and {Timmes}, F.~X. and {Vladimirova}, N.},
    title = "{Mapping Initial Hydrostatic Models in Godunov Codes}",
  journal = {Astrophys J Suppl S},
   eprint = {arXiv:astro-ph/0208031},
 keywords = {Hydrodynamics, Methods: Numerical, Stellar Dynamics},
     year = 2002,
    month = dec,
   volume = 143,
    pages = {539-565},
      doi = {10.1086/342754},
   adsurl = {http://adsabs.harvard.edu/abs/2002ApJS..143..539Z},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}


@ARTICLE{BDS,
   author = {J. B. Bell and C. N. Dawson and G. R. Shubin},
    title = {An unsplit, higher order {G}odunov method for scalar conservation l
aws in
             multiple dimensions},
  journal = JCP,
  volume  = {74},
     year = {1988},
  pages   = {1-24}
}


@article{quadBDS,
   author = {S. May and A. J. Nonaka and A. S. Almgren and J. B. Bell},
   title = {An Unsplit, Higher Order {G}odunov Method Using Quadratic
           Reconstruction for Advection in Multiple Dimensions},
     year ={2011},
  journal ="{Communications in Applied Mathematics and Computational Science}",
  volume = 6,
  number = 1
}

@Book{laney,
  author =       {C. B. Laney},
  title =        {Computational Gasdynamics}, 
  publisher =    {Cambridge},
  year =         {1998},
}

@ARTICLE{athena,
   author = {{Stone}, J.~M. and {Gardiner}, T.~A. and {Teuben}, P. and {Hawley}, J.~F. and 
{Simon}, J.~B.},
    title = "{Athena: A New Code for Astrophysical MHD}",
  journal = {Astrophys J Suppl S},
archivePrefix = "arXiv",
   eprint = {0804.0402},
 keywords = {Hydrodynamics, Magnetohydrodynamics: MHD, Methods: Numerical},
     year = 2008,
    month = sep,
   volume = 178,
    pages = {137-177},
      doi = {10.1086/588755},
   adsurl = {http://adsabs.harvard.edu/abs/2008ApJS..178..137S},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@ARTICLE{colellasekora,
   author = {{Colella}, P. and {Sekora}, M.~D.},
    title = "{A limiter for PPM that preserves accuracy at smooth extrema}",
  journal = {Journal of Computational Physics},
     year = 2008,
    month = jul,
   volume = 227,
    pages = {7069-7076},
      doi = {10.1016/j.jcp.2008.03.034},
   adsurl = {http://adsabs.harvard.edu/abs/2008JCoPh.227.7069C},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@Article{berger-colella,
  author =       {M. J. Berger and P. Colella},
  title =        {Local Adaptive Mesh Refinement for Shock Hydrodynamics},
  journal =      JCP,
  volume =       {82},
  number =       {1},
  pages =        {64--84},
  month =        May,
  year =         {1989},
}

@article{goldberg:1991,
    author = {David Goldberg},
    title = {What Every Computer Scientist Should Know About Floating Point Arithmetic},
    journal = {ACM Computing Surveys},
    year = {1991},
    volume = {23},
    number = {1},
    pages = {5--48}
}


@article{strang,
     jstor_articletype = {research-article},
     title = {On the Construction and Comparison of Difference Schemes},
     author = {Strang, G.},
     journal = {SIAM Journal on Numerical Analysis},
     jstor_issuetitle = {},
     volume = {5},
     number = {3},
     jstor_formatteddate = {Sep., 1968},
     pages = {pp. 506-517},
     url = {http://www.jstor.org/stable/2949700},
     ISSN = {00361429},
     abstract = {},
     language = {English},
     year = {1968},
     publisher = {Society for Industrial and Applied Mathematics},
     copyright = {Copyright © 1968 Society for Industrial and Applied Mathematics},
}

@ARTICLE{ABRZ:I,
   author = {A. S. Almgren and J. B. Bell and C. A. Rendleman and M. Zingale},
    title = "{Low Mach Number Modeling of Type Ia Supernovae. I. Hydrodynamics}",
  journal = {APJ},
     year = 2006,
   volume = 637,
    pages = {922-936},
    month = feb
}

@ARTICLE{ABRZ:II,
   author = {A. S. Almgren and J. B. Bell and C. A. Rendleman and M. Zingale},
    title = "{Low Mach Number Modeling of Type Ia Supernovae. II. Energy Evolution}",
  journal = {APJ},
     year = 2006,
   volume = 649,
    pages = {927-938},
    month = oct
}

@ARTICLE{ABNZ:III,
   author = {{Almgren}, A.~S. and {Bell}, J.~B. and {Nonaka}, A. and
             {Zingale}, M.},
    title = "{Low Mach Number Modeling of Type Ia Supernovae. III. Reactions}",
  journal = {APJ},
     year = 2008,
   volume = 684,
    pages = {449-470},
      doi = {10.1086/590321},
   adsurl = {http://adsabs.harvard.edu/abs/2008ApJ...684..449A},
}


@ARTICLE{SPH,
   author = {{Monaghan}, J.~J.},
    title = "{An introduction to SPH}",
  journal = {Computer Physics Communications},
     year = 1988,
    month = jan,
   volume = 48,
    pages = {89-96},
      doi = {10.1016/0010-4655(88)90026-4},
   adsurl = {http://adsabs.harvard.edu/abs/1988CoPhC..48...89M},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@ARTICLE{arepo,
   author = {{Springel}, V.},
    title = "{E pur si muove: Galilean-invariant cosmological hydrodynamical simulations on a moving mesh}",
  journal = MNRAS,
archivePrefix = "arXiv",
   eprint = {0901.4107},
 primaryClass = "astro-ph.CO",
 keywords = {methods: numerical, galaxies: interactions, cosmology: dark matter},
     year = 2010,
    month = jan,
   volume = 401,
    pages = {791-851},
      doi = {10.1111/j.1365-2966.2009.15715.x},
   adsurl = {http://adsabs.harvard.edu/abs/2010MNRAS.401..791S},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}


@ARTICLE{schulz-rinne:1993,
  author = {{Schulz-Rinne}, C.~W. and {Collins}, J.~P. and {Glaz}, H.~M.},
  title = "{Numerical Solution of the Riemann Problem for Two-Dimensional
            Gas Dynamics}",
  journal = {SIAM J Sci Comput},
  volume = {14},
  number = {6},
  year = {1993},
  pages = {1394-1414}
}

@ARTICLE{pyro,
  author = {{Zingale}, M.},
  title = "{\pyro: A teaching code for computational astrophysical hydrodynamics}",
  journal = {Astronomy and Computing},
  year = 2014,
  note = "accepted for publication"
}

@ARTICLE{byrnehindmarsh,
  author = {{Byrne}, G.~D. and {Hindmarsh}, A.~C.},
  title = "{Stiff ODE Solvers: A Review of Current and Coming Attractions}",
   year = 1986,
  journal = {UCRL-94297 Preprint}
}

@ARTICLE{almgren:2000,
        AUTHOR = {A. Almgren},
        TITLE = {A New Look at the Pseudo-incompressible Solution to
                 {L}amb's problem of Hydrostatic Adjustment},
        JOURNAL = JAS,
        VOLUME = {57},
        MONTH = Apr,
        YEAR = {2000},
        PAGES = {995--998}
}


@ARTICLE{KP:2012,
   author = {Rupert Klein and Olivier Pauluis},
    title = {Thermodynamic Consistency of a Pseudoincompressible Approximation for General Equations of State},
  journal = JAS,
    month = {March},
     year = 2012
}

@ARTICLE{VLBWZ:2013,
   author = {Geoffrey M. Vasil and Daniel Lecoanet and Benjamin P. Brown and Toby S. Wood and Ellen G. Zweibel},
    title = {Energy Conservation and Gravity Waves in Sound-proof Treatments of Stellar Interiors. II.
             Lagrangian Constrained Analysis},
  journal = APJ,
  volume = 773,
  pages = {169-},
     year = 2013
}


@ARTICLE{multilevel,
   author = {A. Nonaka and A. S. Almgren and J. B. Bell and M. J. Lijewski and C. M. Malone and M. Zingale},
    title = {{\tt MAESTRO}:An Adaptive Low Mach Number Hydrodynamics Algorithm for Stellar Flows},
  journal = {APJS},
     year = {2010},
   volume = {188},
    pages = {358-383},
}