Cosmic strings are a fundamental feature of many physically-motivated field theories which inevitably form in the early Universe, as a result of a symmetry breaking phase transition. An important example is the Peccei-Quinn mechanism, from which strings emerge as a potential source of dark matter axions. They are also a strong source of gravitational wave (GW) emission, with the potential for detection by the Laser Interferometer Gravitational-Wave Observatory (LIGO) and other GW experiments.

The nonlinear evolution of cosmic strings has been extensively studied using large-scale numerical simulations. However, the vast difference in scale between a typical string width and the string curvature poses a significant computational challenge. This is usually addressed by approximating the string to have either zero or fixed comoving width, resulting in inconsistencies in predictions between different methods. One technique that can address this issue is adaptive mesh refinement (AMR), which allows the resolution of the numerical grid to adapt to the scale of the features of interest in the simulation. This thesis uses GRChombo, a sophisticated code originally designed for numerical relativity, to perform the first AMR simulations of global cosmic strings. We also present our numerical contributions to GRChombo as a core developer, including novel diagnostic tools and performance enhancement.

We perform a detailed quantitative investigation of single sinusoidally displaced string configurations, comparing oscillating string trajectories with a backreaction model accounting for radiation energy losses. We conclude that analytic radiation modelling in the thin-string (Nambu-Goto) limit provides the appropriate picture for cosmological evolution. We also investigate the resulting massless (Goldstone boson or axion) and massive (Higgs) radiation signals, using quantitative diagnostic tools to determine their eigenmode decomposition. We find that the massless quadrupole is dominant and massive radiation is strongly suppressed with increasing mass, with a complex wavepacket structure that is sensitive to numerical resolution. String network configurations are also simulated, with advanced visualisation of radiation used to reveal new qualitative phenomena as strings reconnect and small loops decay. The thesis concludes with the cosmological implications of this work, considering dark matter axions radiated by cosmic strings and the outlook for gravitational wave signatures.