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Abstract

Numerical methods to solve the Navier-Stokes equations (NSE) are of fundamental importance in theoretical astronomy. In the theory of planet formation, they are used to tackle open problems such as the turbulence-generating mechanisms in protoplanetary disks or the formation of planetesimals from collapsing clouds of pebbles. In the context of stellar interiors, hydrodynamic instabilities described by the NSE are believed to be important in mediating angular momentum transport. This thesis introduces the novel, globally implicit hydrodynamics solver MATRICS. A combination of numerical methods, allowing for extensibility and efficient use in the low Mach number regime, is presented, and its functionality is proven. The MATRICS code is used to conduct the first-ever global simulations of the Goldreich- Schubert-Fricke instability (GSF) in a pressure-supported environment. The GSF is found to operate with analytically expected growth rates in the isothermal case. The predicted dependence on the Prandtl number in the diffusion process-controlled thermalization regime is confirmed. For the first time, hints to the concurrent pres- ence of Convective Overstability (COS) within the same environment are found. GIZMO simulations of collapsing pebble clouds, modeling the Asteroid-and Kuiper-Belt, are also analyzed. The mass distribution of simulated planetesimals at 2.3 AU distance from a solar mass star matches the observed initial mass function (IMF) of asteroids. The size distribution of planetesimals at 25 AU shows an excess of small objects but follows a profile similar to the asteroid’s IMF for larger objects. By incorporating pebble-to-gas coupling, it is confirmed that angular momentum conservation plays the single most important role in determining the planetesimal IMF. Through analysis of their formation history, it is found that many planetesimals are compounds of smaller objects with typical sizes of ∼ 10 − 30 km. This is consistent with recent observations of objects in the Main-/ and Kuiper-Belt.