Axion strings are topological defects that arise in particle physics models with a spontaneously broken global U(1) symmetry, motivated, for example, by the Peccei-Quinn mechanism. They are predicted to radiate massless dark matter axions, massive particles and gravitational waves. If we are to detect axion dark matter in the post-inflationary symmetry breaking scenario, either directly or indirectly via gravitational waves, understanding the magnitude and spectrum of the radiation from a network of strings will be crucial. In this talk, I will detail my work on the analytic modelling of axion string radiation using adaptive mesh refinement simulations. I will focus on my most recent paper, arXiv:2312.07701, which models the radiation from colliding travelling wave configurations with a Gaussian profile and its dependence on parameters such as the amplitude of the Gaussian, and the radius of curvature of the string relative to the string width.