Numerical methods for 3D magneto-rotational core-collapse supernova simulation with jet formation

The work presented in this thesis is devoted to the development of
a numerical model for the three dimensional simulation of magneto-rotational
core-collapse supernovae (MHD-CCSNe) with jet formation.
The numerical model then suggests that MHD-CCSNe naturally provide a
possible site for the strong rapid neutron capture process in agreement with
observations of the early Galactic chemical evolution.
In the first part of this thesis, we develop several numerical methods
and describe thoroughly their efficient implementations on current
high-performance computer architectures.
We develop a fast and simple computer code \texttt{FISH} that solves
the equations of magnetohydrodynamics.
The code is parallelized with an optimal combination of shared and
distributed memory paradigms and scales to several thousands processes
on high-performance computer clusters.
We develop a novel well-balanced numerical scheme for the Euler
equations with gravitational source terms to preserve a discrete hydrostatic
equilibrium exactly.
Being able to accurately represent hydrostatic equilibria is of particular
interest for the simulation of CCSN, because a large part of the newly
forming neutron star evolves in a quasi-hydrostatic manner.
We include an approximate and computationally efficient treatment of
neutrino physics in the form of a spectral leakage scheme.
It enables us to capture approximately the most important neutrino cooling
effects, which are responsible for the shock stall and for the
neutronisation of matter behind the shock.
The latter is crucial for the nucleosynthesis yields.
To fit into our multidimensional MHD-CCSN model, the spectral leakage
scheme is implemented in a ray-by-ray approach.
In the second part of this thesis, we apply our three-dimensional
numerical model to the study of the MHD-CCSN explosion mechanism.
We investigate a series of models with poloidal magnetic field and varying
initial angular momentum distribution through the collapse, bounce and
jet formation phase.
For all computed models, we investigate the process of magnetic field
amplification, angular momentum redisribution and the formation and
driving mechanism of the bipolar outflow.
In a representative model we follow the jet for a longer time and larger
distance.
We find that the bipolar outflow features a significant amount of very
neutron rich matter and is therefore a promising site for the rapid
neutron capture process (r-process).
The computations show that under the prevailing conditions in the bipolarly
ejected matter the global solar r-process pattern could be reproduced.
The computed amount of ejected matter and pecularity of the progenitor
(featuring large enough rotation and magnetic fields to induce MHD-CCSN
explosion mechanism) indicates that only a fraction (perhaps 0.1 - 1\%) of
CCSN explode with the MHD mechanism.
This is also in agreement with the observed large star-to-star scatter of
r-process element abundances in very old halo stars indicating the
scarcity of these events in the early Galactic chemical evolution.