This paper presents lattice simulations to estimate the axion dark matter abundance radiated from global cosmic strings in the post-inflationary scenario. The authors confirm the logarithmic growth in the number of strings per Hubble patch and the spectral index of the power law scaling for the axion spectrum. They discuss the strong correlation between the axion spectrum and string evolutions with different initial conditions, supporting the insensitivity of scaling behaviors against different initial data. The impact of various combinations of the power law of the axion spectrum, nonlinearities around the QCD scale, and average inter-string distances on the axion abundance are discussed. A new novel string identification method based on tetrahedralization is introduced, which guarantees the connectedness of the strings and provides a convenient way of assigning the core location. The authors derive a lower bound on the axion mass. The paper also discusses the cosmological evolution of the string network, the axion spectrum, and the correlation between strings and axion spectrum. The results show that the axion spectrum follows a power law fall-off behavior, and the axion abundance depends on the scaling regime, the power law of the axion spectrum, and the nonlinearities around the QCD scale. The authors conclude that the axion dark matter abundance is sensitive to the scaling regime and the initial conditions, and that the axion mass is bounded from below.This paper presents lattice simulations to estimate the axion dark matter abundance radiated from global cosmic strings in the post-inflationary scenario. The authors confirm the logarithmic growth in the number of strings per Hubble patch and the spectral index of the power law scaling for the axion spectrum. They discuss the strong correlation between the axion spectrum and string evolutions with different initial conditions, supporting the insensitivity of scaling behaviors against different initial data. The impact of various combinations of the power law of the axion spectrum, nonlinearities around the QCD scale, and average inter-string distances on the axion abundance are discussed. A new novel string identification method based on tetrahedralization is introduced, which guarantees the connectedness of the strings and provides a convenient way of assigning the core location. The authors derive a lower bound on the axion mass. The paper also discusses the cosmological evolution of the string network, the axion spectrum, and the correlation between strings and axion spectrum. The results show that the axion spectrum follows a power law fall-off behavior, and the axion abundance depends on the scaling regime, the power law of the axion spectrum, and the nonlinearities around the QCD scale. The authors conclude that the axion dark matter abundance is sensitive to the scaling regime and the initial conditions, and that the axion mass is bounded from below.