[1] High-pressure metamorphic rocks provide evidence that in subduction zones material can return from depths of more than 100 km to the surface. The pressure-temperature paths recorded by these rocks are variable, mostly revealing cooling during decompression, while the time constraints are generally narrow and indicate that the exhumation rates can be on the order of plate velocities. As such, subduction cannot be considered as a single pass process; instead, return flow of a considerable portion of crustal and upper mantle material must be accounted for. Our numerical simulations provide insight into the self-organizing large-scale flow patterns and temperature field of subduction zones, primarily controlled by rheology, phase transformations, fluid budget, and heat transfer, which are all interrelated. They show the development of a subduction channel with forced return flow of low-viscosity material and progressive widening by hydration of the mantle wedge. The large-scale structures and the array of pressure-temperature paths obtained by these simulations favorably compare to the record of natural rocks and the structure of high-pressure metamorphic areas.

Numerical modelling of geodynamic processes was predominantly the domain of high-level mathematicians experienced in numerical and computational techniques. Now, for the first time, students and new researchers in the Earth Sciences can learn the basic theory and applications from a single, accessible reference text. Assuming only minimal prerequisite mathematical training (simple linear algebra and derivatives) the author provides a solid grounding in basic mathematical theory and techniques, including continuum mechanics and partial differential equations, before introducing key numerical and modelling methods. 8 well-documented, state-of–the-art visco-elasto-plastic, 2-D models are then presented, which allow robust modelling of key dynamic processes such as subduction, lithospheric extension, collision, slab break-off, intrusion emplacement, mantle convection and planetary core formation. Incorporating 47 practical exercises and 67 MATLAB examples (for which codes are available online at www.cambridge.org/gerya), this textbook provides a user-friendly introduction for graduate courses or self-study, encouraging readers to experiment with geodynamic models.

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