Abstract: Numerical simulation technology has emerged as a crucial tool for exploring geodynamic processes. This paper reviews the current applicationsof numerical simulations in geodynamics, focusing on key methods, algorithms, and codes, with outlining future development prospects. By discretizing continuous equations and employing numerical algorithms, these simulations efficiently model geological processes and predict dynamic changes in the Earth’s system. The paper systematically discusses the principles, characteristics, and applicable conditions for mainstream numerical methods, including the finite element method, finite difference method, boundary element method, and finite volume method. It explores the finite element method for simulating tectonic stress fields and fault dynamics, the finite difference method for seismic wave propagation, and the boundary element and finite volume methods for fault mechanics and pore fluid flow. A comparative analysis highlights the strengths and weaknesses of each method, indicating that coupling various numerical methods is a key future direction in geodynamics. Furthermore, this paper anticipates the growing significance of numerical simulation technology in Earth system scientific research, propelled by advancements in high-performance computing and the era of big data.

Key words: numerical simulation；geodynamic；geological modeling；numerical methods；Earth system；finite element method, multiphysics coupling simulation