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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.

 

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. 

Abstract This paper provides an overview of the new features of the finite element library deal.II, version 9.4. 

Abstract. Geodynamical simulations over the past decades have widely beenbuilt on quadrilateral and hexahedral finite elements. For thediscretization of the key Stokes equation describing slow, viscousflow, most codes use either the unstable Q1×P0 element, astabilized version of the equal-order Q1×Q1 element, ormore recently the stable Taylor–Hood element with continuous(Q2×Q1) or discontinuous (Q2×P-1)pressure. However, it is not clear which of these choices isactually the best at accurately simulating “typical” geodynamicsituations. Herein, we provide a systematic comparison of all of theseelements for the first time. We use a series of benchmarks that illuminate differentaspects of the features we consider typical of mantle convectionand geodynamical simulations. We will show in particular that the stabilizedQ1×Q1 element has great difficulty producing accuratesolutions for buoyancy-driven flows – the dominant forcing formantle convection flow – and that the Q1×P0 element istoo unstable and inaccurate in practice. As a consequence, webelieve that the Q2×Q1 and Q2×P-1 elementsprovide the most robust and reliable choice for geodynamical simulations,despite the greater complexity in their implementation and thesubstantially higher computational cost when solving linearsystems. 

The traditional workflow in continuum mechanics simulations is that a geometry description —for example obtained using Constructive Solid Geometry (CSG) or Computer Aided Design (CAD) tools—forms the input for a mesh generator. The mesh is then used as the sole input for the finite element, finite volume, and finite difference solver, which at this point no longer has access to the original, “underlying” geometry. However, many modern techniques—for example, adaptive mesh refinement and the use of higher order geometry approximation methods—really do need information about the underlying geometry to realize their full potential. We have undertaken an exhaustive study of where typical finite element codes use geometry information, with the goal of determining what information geometry tools would have to provide. Our study shows that nearly all geometry-related needs inside the simulators can be satisfied by just two “primitives”: elementary queries posed by the simulation software to the geometry description. We then show that it is possible to provide these primitives in all of the frequently used ways in which geometries are described in common industrial workflows, and illustrate our solutions using a number of examples.