References

[Alm00]

A. Almgren. A new look at the pseudo-incompressible solution to Lamb's problem of hydrostatic adjustment. Journal of Atmospheric Science, 57:995–998, April 2000.

[ABC00]

A. S. Almgren, J. B. Bell, and W. Y. Crutchfield. Approximate projection methods: part I. Inviscid analysis. SIAM J. Sci. Comput., 22(4):1139–59, 2000.

[ABS96]

A. S. Almgren, J. B. Bell, and W. G. Szymczak. A numerical method for the incompressible Navier-Stokes equations based on an approximate projection. SIAM J. Sci. Comput., 17(2):358–369, March 1996.

[BCH91]

J. B. Bell, P. Colella, and L. H. Howell. An efficient second-order projection method for viscous incompressible flow. In Proceedings of the Tenth AIAA Computational Fluid Dynamics Conference, 360–367. AIAA, June 1991.

[BDR+04]

J. B. Bell, M. S. Day, C. A. Rendleman, S. E. Woosley, and M. Zingale. Direct numerical simulations of Type Ia supernovae flames I: the Landau-Darrieus instability. \apj , 606:1029, 2004.

[BM92]

J. B. Bell and D. L. Marcus. A second-order projection method for variable-density flows. Journal of Computational Physics, 101(2):334–348, August 1992.

[CF88]

G. R. Caughlan and W. A. Fowler. Thermonuclear reaction rates V. Atomic Data and Nuclear Data Tables, 40(2):283–334, 1988. see also http://www.phy.ornl.gov/astrophysics/data/cf88/index.html.

[CAF+10]

Richard H. Cyburt, A. Matthew Amthor, Ryan Ferguson, Zach Meisel, Karl Smith, Scott Warren, Alexander Heger, R. D. Hoffman, Thomas Rauscher, Alexander Sakharuk, Hendrik Schatz, F. K. Thielemann, and Michael Wiescher. The jina reaclib database: its recent updates and impact on type-i x-ray bursts. \apjs , 189(1):240, 2010. URL: http://stacks.iop.org/0067-0049/189/i=1/a=240.

[DB00]

M. S. Day and J. B. Bell. Numerical simulation of laminar reacting flows with complex chemistry. Combust. Theory Modelling, 4(4):535–556, 2000.

[Dur89]

D. R. Durran. Improving the anelastic approximation. Journal of Atmospheric Science, 46(11):1453–1461, 1989.

[KP12]

Rupert Klein and Olivier Pauluis. Thermodynamic consistency of a pseudoincompressible approximation for general equations of state. JAS, March 2012.

[VLB+13]

Geoffrey M. Vasil, Daniel Lecoanet, Benjamin P. Brown, Toby S. Wood, and Ellen G. Zweibel. Energy conservation and gravity waves in sound-proof treatments of stellar interiors. ii. lagrangian constrained analysis. Astrophysical Journal, 773:169–, 2013.

[AlmgrenBecknerBell+10]

A. S. Almgren, V. E. Beckner, J. B. Bell, M. S. Day, L. H. Howell, C. C. Joggerst, M. J. Lijewski, A. Nonaka, M. Singer, and M. Zingale. CASTRO: A New Compressible Astrophysical Solver. I. Hydrodynamics and Self-gravity. \apj , 715:1221–1238, June 2010. arXiv:1005.0114, doi:10.1088/0004-637X/715/2/1221.

[AlmgrenBellNonakaZingale08]

A. S. Almgren, J. B. Bell, A. Nonaka, and M. Zingale. Low Mach Number Modeling of Type Ia Supernovae. III. Reactions. \apj , 684:449–470, September 2008. doi:10.1086/590321.

[AlmgrenBellRendlemanZingale06a]

A. S. Almgren, J. B. Bell, C. A. Rendleman, and M. Zingale. Low Mach Number Modeling of Type Ia Supernovae. I. Hydrodynamics. \apj , 637:922–936, February 2006. arXiv:arXiv:astro-ph/0509892, doi:10.1086/498426.

[AlmgrenBellRendlemanZingale06b]

A. S. Almgren, J. B. Bell, C. A. Rendleman, and M. Zingale. Low Mach Number Modeling of Type Ia Supernovae. II. Energy Evolution. \apj , 649:927–938, October 2006. arXiv:arXiv:astro-ph/0606496, doi:10.1086/507089.

[AspdenBellDay+08]

A. J. Aspden, J. B. Bell, M. S. Day, S. E. Woosley, and M. Zingale. Turbulence-Flame Interactions in Type Ia Supernovae. ApJ, 689:1173–1185, December 2008. arXiv:0811.2816, doi:10.1086/592726.

[BellColellaGlaz89]

J. B. Bell, P. Colella, and H. M. Glaz. A Second Order Projection Method for the Incompressible Navier-Stokes Equations. Journal of Computational Physics, 85:257, December 1989. doi:10.1016/0021-9991(89)90151-4.

[BellDayRendleman+04]

J. B. Bell, M. S. Day, C. A. Rendleman, S. E. Woosley, and M. A. Zingale. Adaptive low Mach number simulations of nuclear flame microphysics. Journal of Computational Physics, 195:677–694, April 2004. doi:10.1016/j.jcp.2003.10.035.

[ChamulakBrownTimmesDupczak08]

D. A. Chamulak, E. F. Brown, F. X. Timmes, and K. Dupczak. The Reduction of the Electron Abundance during the Pre-explosion Simmering in White Dwarf Supernovae. \apj , 677:160–168, April 2008. arXiv:0801.1643, doi:10.1086/528944.

[FanNonakaAlmgren+19]

Duoming Fan, Andrew Nonaka, Ann S. Almgren, Alice Harpole, and Michael Zingale. MAESTROeX: A Massively Parallel Low Mach Number Astrophysical Solver. arXiv e-prints, pages arXiv:1908.03634, Aug 2019. arXiv:1908.03634.

[FryxellOlsonRicker+00]

B. Fryxell, K. Olson, P. Ricker, F. X. Timmes, M. Zingale, D. Q. Lamb, P. MacNeice, R. Rosner, J. W. Truran, and H. Tufo. FLASH: An Adaptive Mesh Hydrodynamics Code for Modeling Astrophysical Thermonuclear Flashes. \apjs , 131:273–334, November 2000. doi:10.1086/317361.

[JacobsZingaleNonaka+16]

A. M. Jacobs, M. Zingale, A. Nonaka, A. S. Almgren, and J. B. Bell. Low Mach Number Modeling of Convection in Helium Shells on Sub-Chandrasekhar White Dwarfs. II. Bulk Properties of Simple Models. \apj , 827(1):84, Aug 2016. arXiv:1507.06696, doi:10.3847/0004-637X/827/1/84.

[LeVeque02]

R. J. LeVeque. Finite Volume Methods for Hyperbolic Problems. Cambridge Texts in Applied Mathematics. Cambridge University Press, 2002.

[MaloneNonakaAlmgren+11]

C. M. Malone, A. Nonaka, A. S. Almgren, J. B. Bell, and M. Zingale. Multidimensional Modeling of Type I X-ray Bursts. I. Two-dimensional Convection Prior to the Outburst of a Pure $^4$He Accretor. \apj , 728:118–+, February 2011. arXiv:1012.0609, doi:10.1088/0004-637X/728/2/118.

[MaloneZingaleNonaka+14]

C. M. Malone, M. Zingale, A. Nonaka, A. S. Almgren, and J. B. Bell. Multidimensional Modeling of Type I X-Ray Bursts. II. Two-dimensional Convection in a Mixed H/He Accretor. \apj , 788:115, June 2014. doi:10.1088/0004-637X/788/2/115.

[NonakaAlmgrenBell+10]

A. Nonaka, A. S. Almgren, J. B. Bell, M. J. Lijewski, C. M. Malone, and M. Zingale. MAESTRO: An Adaptive Low Mach Number Hydrodynamics Algorithm for Stellar Flows. \apjs , 188:358–383, June 2010. arXiv:1005.0112, doi:10.1088/0067-0049/188/2/358.

[NonakaAspdenZingale+12]

A. Nonaka, A. J. Aspden, M. Zingale, A. S. Almgren, J. B. Bell, and S. E. Woosley. High-resolution Simulations of Convection Preceding Ignition in Type Ia Supernovae Using Adaptive Mesh Refinement. \apj , 745:73, January 2012. arXiv:1111.3086, doi:10.1088/0004-637X/745/1/73.

[NonakaMayAlmgrenBell11]

A. Nonaka, S. May, A. S. Almgren, and J. B. Bell. A Three-Dimensional, Unsplit Godunov Method for Scalar Conservation Laws. SIAM J. Sci. Comput., 33(4):2039–2062, 2011.

[Ricker08]

P. M. Ricker. A Direct Multigrid Poisson Solver for Oct-Tree Adaptive Meshes. \apjs , 176:293–300, May 2008. arXiv:0710.4397, doi:10.1086/526425.

[TurkSmithOishi+11]

M. J. Turk, B. D. Smith, J. S. Oishi, S. Skory, S. W. Skillman, T. Abel, and M. L. Norman. yt: A Multi-code Analysis Toolkit for Astrophysical Simulation Data. \apjs , 192:9, January 2011. arXiv:1011.3514, doi:10.1088/0067-0049/192/1/9.

[WallaceWoosley81]

R. K. Wallace and S. E. Woosley. Explosive hydrogen burning. \apjs , 45:389–420, February 1981. doi:10.1086/190717.

[ZingaleWoosleyRendleman+05]

M Zingale, S. E. Woosley, C. A. Rendleman, M. S. Day, and J. B. Bell. Three-dimensional Numerical Simulations of Rayleigh-Taylor Unstable Flames in Type Ia Supernovae. \apj , 632:1021, 2005.

[ZingaleAlmgrenBell+09]

M. Zingale, A. S. Almgren, J. B. Bell, A. Nonaka, and S. E. Woosley. Low Mach Number Modeling of Type IA Supernovae. IV. White Dwarf Convection. \apj , 704:196–210, October 2009. arXiv:0908.2668, doi:10.1088/0004-637X/704/1/196.

[ZingaleMaloneNonaka+15]

M. Zingale, C. M. Malone, A. Nonaka, A. S. Almgren, and J. B. Bell. Comparisons of Two- and Three-Dimensional Convection in Type I X-Ray Bursts. \apj , 807(1):60, Jul 2015. arXiv:1410.5796, doi:10.1088/0004-637X/807/1/60.

[ZingaleNonakaAlmgren+11]

M. Zingale, A. Nonaka, A. S. Almgren, J. B. Bell, C. M. Malone, and S. E. Woosley. The Convective Phase Preceding Type Ia Supernovae. \apj , 740:8, October 2011. doi:10.1088/0004-637X/740/1/8.