We will talk about our contribution to a large project with the goal of a self-consistent numerical simulation of the evolution of the universe beginning soon after the Big Bang and ending with the formation of realistic stellar systems like the Milky Way. This is a multi-scale problem of vast proportions. It requires the development of new numerical methods that excel in accuracy, parallel scalability, and physical fidelity to the processes relevant in galaxy formation. These numerical methods themselves require the development of mathematical theory in order to guarantee the above mentioned requirements.
In particular we introduce a finite volume code for ideal magnetohydrodynamics (MHD), which possesses excellent stability properties. Ingredients are: an approximate Riemann solver, extension to multidimensions via a Powell term, second order preserving positivity. The scheme’s robustness is due to entropy stability, positivity and properly discretised Powell terms. This can be shown due to a mathematical theory inspired by a kinetic description of the phenomena.
The lecture will be illustrated by movies that show numerical simulations related to the evolution of the universe. This will go beyond our own contributions and also show simulations of my collaborators Volker Springel and Fritz Röpke.
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