With the advent of the era of big data, the framework of numerical method of computational geodynamics is perfected. In this paper, we review systematically the conventional numerical simulation methods in the field of computational geodynamics, included the finite-difference, finite-element, spectral method, and spectral element methods. In addition, some newly developed algorithms and their applications in recent years are reviewed, such as the discontinuous Galerkin methods, wavelet method, and lattice Boltzmann method. We hope that the review can give a holistic perspective to understand the development context of the numerical methods of geodynamics and provide a useful reference for studying and adapting to increasingly rich data and new algorithms in the era of big data.
