References

[BBH89]

P. N. Brown, G. D. Byrne, and A. C. Hindmarsh. VODE: a variable coefficient ode solver. SIAM J. Sci. Stat. Comput., 10:1038–1051, 1989.

[CTS+07]

A. C. Calder, D. M. Townsley, I. R. Seitenzahl, F. Peng, O. E. B. Messer, N. Vladimirova, E. F. Brown, J. W. Truran, and D. Q. Lamb. Capturing the fire: flame energetics and neutronization for type ia supernova simulations. The Astrophysical Journal, 656(1):313–332, feb 2007. URL: https://doi.org/10.1086/510709, doi:10.1086/510709.

[CP98]

Gilles Chabrier and Alexander Y. Potekhin. Equation of state of fully ionized electron-ion plasmas. Physical Review E, 58(4):4941–4949, oct 1998. URL: https://doi.org/10.1103, doi:10.1103/physreve.58.4941.

[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.

[GH13]

M W Guidry and J A Harris. Explicit integration of extremely stiff reaction networks: quasi-steady-state methods. Computational Science & Discovery, 6(1):015002, jan 2013. URL: https://dx.doi.org/10.1088/1749-4699/6/1/015002, doi:10.1088/1749-4699/6/1/015002.

[LMP01]

K. LANGANKE and G. MARTÍNEZ-PINEDO. Rate tables for the weak processes of pf-shell nuclei in stellar environments. Atomic Data and Nuclear Data Tables, 79(1):1–46, 2001. doi:https://doi.org/10.1006/adnd.2001.0865.

[Lea18]

Allan M. M. Leal. Autodiff, a modern, fast and expressive C++ library for automatic differentiation. \texttt https://autodiff.github.io, 2018. URL: https://autodiff.github.io.

[MOvanLeer00]

David R. Mott, Elaine S. Oran, and Bram van Leer. A quasi-steady-state solver for the stiff ordinary differential equations of reaction kinetics. Journal of Computational Physics, 164(2):407–428, 2000. doi:https://doi.org/10.1006/jcph.2000.6605.

[SSV98]

B.P. Sommeijer, L.F. Shampine, and J.G. Verwer. RKC: An explicit solver for parabolic PDEs. Journal of Computational and Applied Mathematics, 88(2):315–326, March 1998. URL: https://linkinghub.elsevier.com/retrieve/pii/S0377042797002197, doi:10.1016/S0377-0427(97)00219-7.

[ZKNR22]

M. Zingale, M. P. Katz, A. Nonaka, and M. Rasmussen. An improved method for coupling hydrodynamics with astrophysical reaction networks. The Astrophysical Journal, 936(1):6, aug 2022. URL: https://dx.doi.org/10.3847/1538-4357/ac8478, doi:10.3847/1538-4357/ac8478.

[ZCJ+24]

Michael Zingale, Zhi Chen, Eric T. Johnson, Max P. Katz, and Alexander Smith Clark. Strong coupling of hydrodynamics and reactions in nuclear statistical equilibrium for modeling convection in massive stars. The Astrophysical Journal, 977(1):30, nov 2024. URL: https://dx.doi.org/10.3847/1538-4357/ad8a66, doi:10.3847/1538-4357/ad8a66.

[AlastueyJancovici78]

A. Alastuey and B. Jancovici. Nuclear reaction rate enhancement in dense stellar matter. \apj , 226:1034–1040, December 1978. doi:10.1086/156681.

[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.

[ChugunovDewitt09]

A. I. Chugunov and H. E. Dewitt. Nuclear fusion reaction rates for strongly coupled ionic mixtures. \prc , 80(1):014611, July 2009. arXiv:0905.3844, doi:10.1103/PhysRevC.80.014611.

[ChugunovDewittYakovlev07]

A. I. Chugunov, H. E. Dewitt, and D. G. Yakovlev. Coulomb tunneling for fusion reactions in dense matter: Path integral MonteCarlo versus mean field. \prd , 76(2):025028, July 2007. arXiv:0707.3500, doi:10.1103/PhysRevD.76.025028.

[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.

[GraboskeDewittGrossmanCooper73]

H. C. Graboske, H. E. Dewitt, A. S. Grossman, and M. S. Cooper. Screening Factors for Nuclear Reactions. II. Intermediate Screen-Ing and Astrophysical Applications. \apj , 181:457–474, April 1973. doi:10.1086/152062.

[ItohTotsujiIchimaruDewitt79]

N. Itoh, H. Totsuji, S. Ichimaru, and H. E. Dewitt. Enhancement of thermonuclear reaction rate due to strong screening. II - Ionic mixtures. \apj , 234:1079–1084, December 1979. doi:10.1086/157590.

[Jancovici77]

B. Jancovici. Pair correlation function in a dense plasma and pycnonuclear reactions in stars. Journal of Statistical Physics, 17(5):357–370, November 1977. doi:10.1007/BF01014403.

[KushnirKatz20]

Doron Kushnir and Boaz Katz. An accurate and efficient numerical calculation of detonation waves in multidimensional supernova simulations using a burning limiter and adaptive quasi-statistical equilibrium. Monthly Notices of the Royal Astronomical Society, 493(4):5413–5433, April 2020. arXiv:1912.06151.

[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. arXiv:1404.6286, doi:10.1088/0004-637X/788/2/115.

[ShenBildsten09]

K. J. Shen and L. Bildsten. Unstable Helium Shell Burning on Accreting White Dwarfs. \apj , 699:10, March 2009. arXiv:0903.0654v2.

[TimmesArnett99]

F. X. Timmes and D. Arnett. The Accuracy, Consistency, and Speed of Five Equations of State for Stellar Hydrodynamics. ApJS, 125:277–294, November 1999. doi:10.1086/313271.

[TimmesSwesty00]

F. X. Timmes and F. D. Swesty. The Accuracy, Consistency, and Speed of an Electron-Positron Equation of State Based on Table Interpolation of the Helmholtz Free Energy. ApJS, 126:501–516, February 2000. doi:10.1086/313304.

[WallaceWoosley81]

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

[WallaceWoosleyWeaver82]

R. K. Wallace, S. E. Woosley, and T. A. Weaver. The thermonuclear model for X-ray transients. \apj , 258:696–715, July 1982. doi:10.1086/160119.

[YakovlevGasquesAfanasjev+06]

D. G. Yakovlev, L. R. Gasques, A. V. Afanasjev, M. Beard, and M. Wiescher. Fusion reactions in multicomponent dense matter. \prc , 74(3):035803, September 2006. arXiv:astro-ph/0608488, doi:10.1103/PhysRevC.74.035803.

[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.

[ZingaleKatzBell+19]

M. Zingale, M. P. Katz, J. B. Bell, M. L. Minion, A. J. Nonaka, and W. Zhang. Improved Coupling of Hydrodynamics and Nuclear Reactions via Spectral Deferred Corrections. arXiv e-prints, pages arXiv:1908.03661, Aug 2019. arXiv:1908.03661.

[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 , 807:60, July 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.