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College of Arts and Sciences \departmentDepartment of Scientific Computing \manuscripttypeDissertation \degreeDoctor of Philosophy \degreeyear2023 \defensedateApril 3rd, 2023 \committeepersonTomasz PlewaProfessor Directing Traffic \committeepersonMark SussmanUniversity Representative \committeepersonAdrian BarbuCommittee Member \committeepersonBryan QuaifeCommittee Member \committeepersonOlmo ZavalaCommittee Member

Toward Data-Driven Subgrid-Scale Modeling of the Zel’dovich Deflagration-To-Detonation Mechanism in Dense Stellar Plasmas

Brandon L. Gusto

Abstract

A novel, data-driven model of deflagration-to-detonation transition (DDT) is constructed for application to explosions of thermonuclear supernovae (SN Ia). The DDT mechanism has been suggested as the necessary physics process to obtain qualitative agreement between SN Ia observations and computational explosion models. This work builds upon a series of studies of turbulent combustion that develops during the final stages of the SN explosion. These studies suggest that DDT can occur in the turbulerized flame of the white dwarf via the Zel’dovich reactivity gradient mechanism when hotspots are formed. We construct a large database of direct numerical simulations that explore the parameter space of the Zel’dovich initiated detonation. We use this database to construct a neural network classifier for hotspots. The classifier is integrated into our supernova simulation code, FLASH/Proteus, and is used as the basis for a subgrid-scale model for DDT. The classifier is evaluated both in the training environment and in reactive turbulence simulations to verify its accuracy in realistic conditions.

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{dedication}

This dissertation is dedicated to my loving family: to my mother and father, Renee and Jeffrey, my older brother, Cody, and my little sister, Jenna. Also to my wonderful fiancé, Marie. Finally, of course to my Oma who never expected anything less than a doctorate degree. Without their love and support this manuscript would not have been possible.

Acknowledgements.

The author would like to first acknowledge the Science, Mathematics, and Research for Transformation (SMART) Scholarship-for-Service Program for providing support for this work. Additionally, he would like to thank his advisor, Dr. Tomasz Plewa for his unwavering support and guidance; Tomasz’s dedication to his students and his passion for scientific truth has been a constant source of inspiration. The author also would like to thank Dr. Christoph Federrath from the Australian National University for his help in establishing turbulence driving parameters over many constructive virtual meetings.

{listofsymbols}

$t$	time
$x$	spatial coordinate
$S_{L}$	the laminar flame speed
$\tau$	induction time
$u_{sp}$	reactive wave speed
$z$	reactive wave speed normalized by local soundspeed
$c$	speed of sound
$D_{CJ}$	velocity of a Chapman-Jouget detonation
$\rho$	density
$\rho_{\mathrm{amb}}$	ambient density
$T_{\mathrm{amb}}$	ambient temperature
$\delta\rho$	amplitude of density perturbation
$R$	width of density perturbation
$A$	normalized amplitude of density perturbation
$u$	velocity
$p$	pressure
$\bm{X}$	species concentrations
$X_{f}$	fuel concentration
$\bm{R}$	species reaction rates
$\dot{Q}$	nuclear energy generation term
$\Delta x$	mesh resolution
$N$	number of computational cells
$\bm{U}$	approximate solution
$\hat{\bm{F}}$	numerical fluxes
$\hat{\bm{S}}$	numerical source terms
$\bm{\phi}$	exact solution
$r_{0}$	radius of hotspot region
$r_{s}$	distance from the center of the hotspot to the point where the reactive wave speed equals the soundspeed
$r_{s}^{*}$	the critical value of $r_{s}$ below which detonation cannot occur
$\sigma_{0}$	standard deviation of induction times in hotspot region
$c_{0}$	soundspeed in hotspot region
$\varepsilon$	threshold for defining size of hotspot region
$\Delta_{\mathrm{wd}}$	ILES filter cutoff for the full-star explosion scale of the white dwarf
$\Delta_{\mathrm{tb}}$	ILES filter cutoff for the turbulence-in-a-box scale
$q$	actual label of a neural network input sample
$\hat{q}$	predicted label of a neural network input sample
$\bm{\chi}$	data of a neural network input sample
$\varphi$	activation function
$b$	layer biases
$w$	layer weights
$\ell$	network layer number
$n_{s}$	number of training samples
$n_{x}$	number of spatial points in the input data
$n_{ch}$	number of input channels in a convolutional network
$\delta_{t}$	time delay between network prediction and actual detonation
$\delta_{x}$	spatial distance between loction where network prediction made and estimated detonation origin