Doctoral Dissertations

Orcid ID

0000-0003-1891-8402

Date of Award

8-2024

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Physics

Major Professor

Anthony Mezzacappa

Committee Members

Andrew Steiner, Raph Hix, Vasilios Alexiades, Eric Lentz, Eirik Endeve

Abstract

Core-collapse supernovae (CCSNe) are some of the most extreme and complex phenomena in the universe. The toolkit for high-order neutrino-radiation hydrodynamics (thornado) is being developed to simulate CCSNe which will provide insight into the mechanisms underlying these events. The thornado framework is a collection of modules used to calculate the effects of gravity, hydrodynamics, neutrino transport, and nuclear physics through the Weaklib equation of state table. This dissertation will present the development of the Poseidon code, which provides the general relativistic gravity solver for the thornado framework.

The Poseidon code solves for the general relativistic metric using the xCFC formulation of the Einstein equations. The first part of this dissertation will present the derivation of the xCFC metric equations. This will be done by first casting the Einstein equations in the 3+1 formalism and applying the conformally flat approximation (CFA). The CFA system of equations suffers from non-uniqueness properties, therefore a further approximation is made to arrive at the xCFC system of equations for the metric variables ψ, the conformal factor; α, the lapse function; and β, the shift vector.

The xCFC equations involve two types of equations, non-linear scalar Laplacians, and linear vector Laplacians. Poseidon uses Galerkin projections with real spherical harmonics and radial finite element polynomials to discretize both types of equations. The Fixed-point iteration method with Anderson acceleration is used to solve the non-linear equations that govern the non-linear equations. We will also discuss the coupling of Poseidon with thornado’s hydrodynamics and the incorporation of the adaptive mesh refinement framework, AMReX.

We also present results from Poseidon and the coupled thornado-Poseidon framework. These results include the evolution of realistic stellar progenitors through collapse, core bounce, and the subsequent outward shock propagation. These simulations are done using relativistic hydrodynamics and gravity, and the Weaklib tabulated equation of state table and reveal the importance of relativity on the simulation of CCSNe.

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