Advances and perspectives in numerical modeling for geodynamics

The dynamic processes in Earth’s deep interior are key driving forces behind geological events and play a fundamental role in Earth’s evolution. Their mechanisms and surface responses have been central questions in solid-earth science. Geodynamic modeling, which uses either laboratory or numerical models, is employed to investigate these mechanisms and their surface responses. These models provide physical frameworks for understanding Earth’s internal processes, plate tectonics, formation of earthquakes and volcanism, and the evolution of the Earth system. Compared to physical models done in laboratories, numerical models are more efficient at solving complex geological problems and have become a key method in modern geodynamic research. With significant advances in geophysics, applied mathematics, computational science, and their cross-disciplinary applications, the theories and methods of numerical modeling for geodynamics have significantly progressed over recent decades. Numerical models have been successfully applied to many geological problems, offering new insights into plate tectonics, subduction, plume, and continental dynamics. This review systematically outlines the history and development of numerical modeling in geodynamics, briefly explains its principles and basic methods, and summarizes recent advancements and real-world applications. At the end, this review discusses current challenges and possible future directions for numerical modeling in geodynamics.