In the lower crust, viscous compaction is known to produce solitary porosity and fluid pressure waves. Metamorphic (de)volatilization reactions can also induce porosity changes in response to the propagating fluid pressure anomalies. Here we present results from high‐resolution simulations using Graphic Processing Unit parallel processing with a model that includes both viscous (de)compaction and reaction‐induced porosity changes. Reactive porosity waves propagate in a manner similar to viscous porosity waves, but through a different mechanism involving fluid release and trap in the solid by reaction. These waves self‐generate from red noise or an ellipsoidal porosity anomaly with the same characteristic size and abandon their source region to propagate at constant velocity. Two waves traveling at different velocities pass through each other in a soliton‐like fashion. Reactive porosity waves thus provide an additional mechanism for fluid extraction at shallow depths with implications for ore formation, diagenesis, metamorphic veins formation, and fluid extraction from subduction zones.

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Abstract. The development of highly efficient, robust and scalable numerical algorithms lags behind the rapid increase in massive parallelism of modern hardware. We address this challenge with the accelerated pseudo-transient iterative method and present here a physically motivated derivation. We analytically determine optimal iteration parameters for a variety of basic physical processes and confirm the validity of theoretical predictions with numerical experiments. We provide an efficient numerical implementation of pseudo-transient solvers on graphical processing units (GPUs) using the Julia language. We achieve a parallel efficiency over 96 % on 2197 GPUs in distributed memory parallelisation weak scaling benchmarks. 2197 GPUs allow for unprecedented terascale solutions of 3D variable viscosity Stokes flow on 49953 grid cells involving over 1.2 trillion degrees of freedom. We verify the robustness of the method by handling contrasts up to 9 orders of magnitude in material parameters such as viscosity, and arbitrary distribution of viscous inclusions for different flow configurations. Moreover, we show that this method is well suited to tackle strongly nonlinear problems such as shear-banding in a visco-elasto-plastic medium. A GPU-based implementation can outperform CPU-based direct-iterative solvers in terms of wall-time even at relatively low resolution. We additionally motivate the accessibility of the method by its conciseness, flexibility, physically motivated derivation and ease of implementation. This solution strategy has thus a great potential for future high-performance computing applications, and for paving the road to exascale in the geosciences and beyond.

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