Numerical Methods for Simulations of Planetary Impacts

Abstract

Computational simulations are an invaluable tool for studying the complex processes that shape planetary systems. This includes the impact events, both small and giant, whose lasting effects can be observed throughout the solar system to this day. This work details the development and validation of numerical methods for smoothed particle hydrodynamics (SPH) simulations, and the application of these methods to simulations of planetary impacts.

With traditional SPH formulations, fluid mixing and instability growth are artificially suppressed by spurious surface tension-like effects. The suppression of mixing between dissimilar, stiff materials, such as those used in planetary impact simulations, is especially strong and difficult to alleviate. While various approaches have been developed to mitigate this issue, they often introduce dependencies on specific material properties, rely on targeted or contrived corrections, or require bespoke particle configurations that cannot be maintained throughout the course of typical science simulations. In this thesis, a new SPH formalism is developed. By directly targeting sources of error, this generalised, material-independent approach improves the treatment both of mixing within a single material, for example in an ideal gas, and at interfaces between dissimilar materials. This new SPH scheme is validated in a range of hydrodynamic test simulations, including both standard test cases and planetary-specific scenarios.

These methods are then applied in simulations of planetary giant impacts onto Jupiter to investigate whether this mechanism could be responsible for the planet's observed dilute core. With these new methods, there is a significant increase in the amount of mixing between core and envelope material during impact simulations. Although core material is temporarily diluted, heavy elements settle under gravity and no dilute core is produced in any of the giant impact simulations carried out with different impact speeds, impact angles, internal structures, equations of state, or numerical resolutions.

The capabilities of the newly developed methods are extended to include solid-body mechanics. By incorporating physical models for elasticity, plastic deformation, and fracturing, impacts at much smaller scales can be simulated. The implementation of these models is validated in a range of test simulations.