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Abstract Geodynamic simulations underpin our understanding of upper‐mantle processes, but their predictions require validation against observational data. Widely used geophysical datasets provide limited constraints on dynamic processes into the geological past, whereas under‐exploited geochemical observations from volcanic lavas at Earth's surface constitute a valuable record of mantle processes back in time. Here, we describe a new peridotite‐melting parameterization, BDD21, that can predict the incompatible‐element concentrations of melts within geodynamic simulations, thereby providing a means to validate these simulations against geochemical datasets. Here, BDD21's functionality is illustrated using the Fluidity computational modeling framework, although it is designed so that it can be integrated with other geodynamic software. To validate our melting parameterization and coupled geochemical‐geodynamic approach, we develop 2‐D single‐phase flow simulations of melting associated with passive upwelling beneath mid‐oceanic ridges and edge‐driven convection adjacent to lithospheric steps. We find that melt volumes and compositions calculated for mid‐oceanic ridges at a range of mantle temperatures and plate spreading rates closely match those observed at present‐day ridges with the same conditions. Our lithospheric step simulations predict spatial and temporal melting trends that are consistent with those recorded at intraplate volcanic provinces in similar geologic settings. Taken together, these results suggest that our coupled geochemical‐geodynamic approach can accurately predict a suite of present‐day geochemical observations. Since our results are sensitive to small changes in upper‐mantle thermal and compositional structure, this novel approach provides a means to improve our understanding of the mantle's thermo‐chemical structure and flow regime into the geological past. 

Abstract. Many geodynamical models are formulated in terms of the Stokes equations that are then coupled to other equations. For the numerical solution of the Stokes equations, geodynamics codes over the past decades have used essentially every finite element that has ever been proposed for the solution of this equation, on both triangular/tetrahedral (“simplex”) and quadrilaterals/hexahedral (“hypercube”) meshes. However, in many and perhaps most cases, the specific choice of element does not seem to have been the result of careful benchmarking efforts but based on implementation efficiency or the implementers' background. In a first part of this paper (Thieulot and Bangerth, 2022), we have provided a comprehensive comparison of the accuracy and efficiency of the most widely used hypercube elements for the Stokes equations. We have done so using a number of benchmarks that illustrate “typical” geodynamic situations, specifically taking into account spatially variable viscosities. Our findings there showed that only Taylor–Hood-type elements with either continuous (Q2×Q1) or discontinuous (Q2×P-1) pressure are able to adequately and efficiently approximate the solution of the Stokes equations. In this, the second part of this work, we extend the comparison to simplex meshes. In particular, we compare triangular Taylor–Hood elements against the MINI element and one often referred to as the “Crouzeix–Raviart” element. We compare these choices against the accuracy obtained on hypercube Taylor–Hood elements with approximately the same computational cost. Our results show that, like on hypercubes, the Taylor–Hood element is substantially more accurate and efficient than the other choices. Our results also indicate that hypercube meshes yield slightly more accurate results than simplex meshes but that the difference is relatively small and likely unimportant given that hypercube meshes often lead to slightly denser (and consequently more expensive) matrices. 

The Geodynamic World Builder (GWB) is an open source code library intended to set up initial conditions for computational geodynamic models and/or visualize complex 3d teconic setting, in both Cartesian and Spherical geometries. The inputs for the JSON-style parameter file are not mathematical, but rather a structured nested list describing tectonic features, e.g. a continental, an oceanic or a subducting plate. Each of these tectonic features can be assigned a specific temperature profile (e.g. plate model) or composition label (e.g. uniform). For each point in space, the GWB can return the composition and/or temperature. It is written in C++, but can be used in almost any language through its C, Python and Fortran wrappers. Various examples of 2D and 3D subduction settings are presented. 

Quantifying the depths and temperatures from which igneous rocks are derived is an important step in understanding volcanic, magmatic and mantle processes. We present meltPT, a Python package that allows users to apply twelve published whole-rock thermobarometers within a consistent framework, as well as combine thermobarometric results and geothermal models to estimate mantle potential temperatures. We apply meltPT to basaltic rocks from mid-ocean ridges and the Hawaiian Islands. We find mid-ocean ridge basalts equilibrate between 1–2 GPa and 1275–1475 ℃, corresponding to an ambient mantle potential temperature of ~1400 ℃. We estimate that the Hawaiian plume has an excess temperature of ~150 ℃. Hawaiian melt-equilibration depths increase from 1–3 GPa to 2.5–5 GPa through each island's life cycle. Our results indicate that multiple lithologies are present within the plume, and that transient plume reconfiguration in response to changing plate velocity is a viable mechanism for generating Hawaiʻi's two geochemically distinct plume tracks. 

We are pleased to announce the release of ASPECT 2.5.0. ASPECT is the Advanced Solver for Problems in Earth's ConvecTion. It uses modern numerical methods such as adaptive mesh refinement, multigrid solvers, and a modular software design to provide a fast, flexible, and extensible mantle convection solver. ASPECT is available from https://aspect.geodynamics.org/ and the release is available from https://geodynamics.org/resources/aspect and https://github.com/geodynamics/aspect/releases/tag/v2.5.0 Among others this release includes the following significant changes: ASPECT now includes version 0.5.0 of the Geodynamic World Builder. (Menno Fraters and other contributors) ASPECT's manual has been converted from LaTeX to Markdown to be hosted as a website at https://aspect-documentation.readthedocs.io. (Chris Mills, Mack Gregory, Timo Heister, Wolfgang Bangerth, Rene Gassmoeller, and many others) New: ASPECT now requires deal.II 9.4 or newer. (Rene Gassmoeller, Timo Heister) ASPECT now supports a DebugRelease build type that creates a debug build and a release build of ASPECT at the same time. It can be enabled by setting the CMake option CMAKE_BUILD_TYPE to DebugRelease or by typing "make debugrelease". (Timo Heister) ASPECT now has a CMake option ASPECT_INSTALL_EXAMPLES that allows building and install all cookbooks and benchmarks. ASPECT now additionally installs the data/ directory. Both changes are helpful for installations that are used for teaching and tutorials. (Rene Gassmoeller) Changed: ASPECT now releases the memory used for storing initial conditions and the Geodynamic World Builder after model initialization unless an owning pointer to these objects is kept. This reduces the memory footprint for models initialized from large data files. (Wolfgang Bangerth) Added: Various helper functions to distinguish phase transitions for different compositions and compositional fields of different types. (Bob Myhill) Added: The 'adiabatic' initial temperature plugin can now use a spatially variable top boundary layer thickness read from a data file or specified as a function in the input file. Additionally, the boundary layer temperature can now also be computed following the plate cooling model instead of the half-space cooling model. (Daniel Douglas, John Naliboff, Juliane Dannberg, Rene Gassmoeller) New: ASPECT now supports tangential velocity boundary conditions with GMG for more geometries, such as 2D and 3D chunks. (Timo Heister, Haoyuan Li, Jiaqi Zhang) New: Phase transitions can now be deactivated outside a given temperature range specified by upper and lower temperature limits for each phase transition. This allows implementing complex phase diagrams with transitions that intersect in pressure-temperature space. (Haoyuan Li) New: There is now a postprocessor that outputs the total volume of the computational domain. This can be helpful for models using mesh deformation. (Anne Glerum) New: Added a particle property 'grain size' that tracks grain size evolution on particles using the 'grain size' material model. (Juliane Dannberg, Rene Gassmoeller) Fixed: Many bugs, see link below for a complete list. (Many authors. Thank you!). A complete list of all changes and their authors can be found at https://aspect.geodynamics.org/doc/doxygen/changes_between_2_84_80_and_2_85_80.html Wolfgang Bangerth, Juliane Dannberg, Menno Fraters, Rene Gassmoeller, Anne Glerum, Timo Heister, Bob Myhill, John Naliboff, and many other contributors.