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Abstract Mineral phase transitions can either hinder or accelerate mantle flow. In the present day, the formation of the bridgmanite + ferropericlase assemblage from ringwoodite at 660 km depth has been found to cause weak and intermittent layering of mantle convection. However, for the higher temperatures in Earth's past, different phase transitions could have controlled mantle dynamics. We investigate the potential changes in convection style during Earth's secular cooling using a new numerical technique that reformulates the energy conservation equation in terms of specific entropy instead of temperature. This approach enables us to accurately include the latent heat effect of phase transitions for mantle temperatures different from the average geotherm, and therefore fully incorporate the thermodynamic effects of realistic phase transitions in global‐scale mantle convection modeling. We set up 2‐D models with the geodynamics softwareAspect, using thermodynamic properties computed by HeFESTo, while applying a viscosity profile constrained by the geoid and mineral physics data and a visco‐plastic rheology to reproduce plate‐like behavior and Earth‐like subduction morphologies. Our model results reveal the layering of plumes induced by the wadsleyite to garnet (majorite) + ferropericlase endothermic transition (between 450 and 590 km depth and over the 2000–2500 K temperature range). They show that this phase transition causes a large‐scale and long‐lasting temperature elevation in a depth range of 500–650 km depth if the potential temperature of the mantle is higher than 1800 K, indicating that mantle convection may have been partially layered in Earth's early history. 

This paper provides an overview of the new features of the finite element library deal.II, version 9.6. 

Abstract. Numerical models are a powerful tool for investigating the dynamic processes in the interior of the Earth and other planets, but the reliability and predictive power of these discretized models depends on the numerical method as well as an accurate representation of material properties in space and time. In the specific context of geodynamic models, particle methods have been applied extensively because of their suitability for advection-dominated processes and have been used in applications such as tracking the composition of solid rock and melt in the Earth's mantle, fluids in lithospheric- and crustal-scale models, light elements in the liquid core, and deformation properties like accumulated finite strain or mineral grain size, along with many applications outside the Earth sciences. There have been significant benchmarking efforts to measure the accuracy and convergence behavior of particle methods, but these efforts have largely been limited to instantaneous solutions, or time-dependent models without analytical solutions. As a consequence, there is little understanding about the interplay of particle advection errors and errors introduced in the solution of the underlying transient, nonlinear flow equations. To address these limitations, we present two new dynamic benchmarks for transient Stokes flow with analytical solutions that allow us to quantify the accuracy of various advection methods in nonlinear flow. We use these benchmarks to measure the accuracy of our particle algorithm as implemented in the ASPECT geodynamic modeling software against commonly employed field methods and analytical solutions. In particular, we quantify if an algorithm that is higher-order accurate in time will allow for better overall model accuracy and verify that our algorithm reaches its intended optimal convergence rate. We then document that the observed increased accuracy of higher-order algorithms matters for geodynamic applications with an example of modeling small-scale convection underneath an oceanic plate and show that the predicted place and time of onset of small-scale convection depends significantly on the chosen particle advection method. Descriptions and implementations of our benchmarks are openly available and can be used to verify other advection algorithms. The availability of accurate, scalable, and efficient particle methods as part of the widely used open-source code ASPECT will allow geodynamicists to investigate complex time-dependent geodynamic processes such as elastic deformation, anisotropic fabric development, melt generation and migration, and grain damage. 

SUMMARY The Earth’s magnetic field is generated by a dynamo in the outer core and is crucial for shielding our planet from harmful radiation. Despite the established importance of the core–mantle boundary (CMB) heat flux as driver for the dynamo, open questions remain about how heat flux heterogeneities affect the magnetic field. Here, we explore the distribution of the CMB heat flux on Earth and its changes over time using compressible global 3-D mantle convection models in the geodynamic modelling software ASPECT. We discuss the use of the consistent boundary flux method as a tool to more accurately compute boundary heat fluxes in finite element simulations and the workflow to provide the computed heat flux patterns as boundary conditions in geodynamo simulations. Our models use a plate reconstruction throughout the last 1 billion years—encompassing the complete supercontinent cycle—to determine the location and sinking speed of subducted plates. The results show how mantle upwellings and downwellings create localized heat flux anomalies at the CMB that can vary drastically over Earth’s history and depend on the properties and evolution of the lowermost mantle as well as the surface subduction zone configuration. The distribution of hot and cold structures at the CMB changes throughout the supercontinent cycle in terms of location, shape and number, indicating that these structures fluctuate and might have looked very differently in Earth’s past. We estimate the resulting amplitude of spatial heat flux variations, expressed by the ratio of peak-to-peak amplitude to average heat flux, q*, to be at least 2. However, depending on the material properties and the adiabatic heat flux out of the core, q* can easily reach values >30. For a given set of material properties, q* generally varies by 30–50 per cent over time. Our results have implications for understanding the Earth’s thermal evolution and the stability of its magnetic field over geological timescales. They provide insights into the potential effects of the mantle on the magnetic field and pave the way for further exploring questions about the nucleation of the inner core and the past state of the lowermost mantle. 

Abstract Determining the fate of subducted oceanic crust is critical for understanding material cycling through Earth’s deep interior and sources of mantle heterogeneity. A key control on the distribution of subducted slabs over long timescales is the bridgmanite to post-perovskite phase transition in the lowermost mantle, thought to cause rheological weakening. Using high-resolution computational models, we show that the ubiquitous presence of weak post-perovskite at the core-mantle boundary can facilitate or prevent the accumulation of basaltic oceanic crust, depending on the amount of weakening and the crustal thickness. Moderately weak post-perovskite ( ~ 10–100× weaker) facilitates segregation of crust from subducted slabs, increasing basalt accumulation in dense piles. Conversely, very weak post-perovskite (more than 100× weaker) promotes vigorous plumes that entrain more crustal material, decreasing basalt accumulation. Our results reconcile the contradicting conclusions of previous studies and provide insights into the accumulation of subducted crust in the lowermost mantle throughout Earth’s history. 

Abstract The amount of vapor in the impact-generated protolunar disk carries implications for the dynamics, devolatilization, and moderately volatile element isotope fractionation during lunar formation. The equation of state (EoS) used in simulations of the giant impact is required to calculate the vapor mass fraction (VMF) of the modeled protolunar disk. Recently, a new version of M-ANEOS (Stewart M-ANEOS) was released with an improved treatment of heat capacity and expanded experimental Hugoniot. Here, we compare this new M-ANEOS version with a previous version (N-SPH M-ANEOS) and assess the resulting differences in smoothed particle hydrodynamics (SPH) simulations. We find that Stewart M-ANEOS results in cooler disks with smaller values of VMF and in differences in disk mass that are dependent on the initial impact angle. We also assess the implications of the minimum “cutoff” density (ρ_c), similar to a maximum smoothing length, that is set as a fast-computing alternative to an iteratively calculated smoothing length. We find that the low particle resolution of the disk typically results in >40% of disk particles falling toρ_c, influencing the dynamical evolution and VMF of the disk. Our results show that the choice of EoS,ρ_c, and particle resolution can cause the VMF and disk mass to vary by tens of percent. Moreover, small values ofρ_cproduce disks that are prone to numerical instability and artificial shocks. We recommend that future giant impact SPH studies review smoothing methods and ensure the thermodynamic stability of the disk over simulated time. 

Abstract. Due to the increasing availability of high-performance computing over the past few decades, numerical models have become an important tool for research in geodynamics.Several generations of mantle convection software have been developed, but due to their differing methods and increasing complexity it is important to evaluate the accuracy of each new model generation to ensure published geodynamic research is reliable and reproducible.Here we explore the accuracy of the open-source, finite-element codes ASPECT and CitcomS as a function of mesh spacing using low to moderate-Rayleigh-number models in steady-state thermal convection.ASPECT (Advanced Solver for Problems in Earth's ConvecTion) is a new-generation mantle convection code that enables modeling global mantle convection with realistic parameters and complicated physical processes using adaptive mesh refinement (Kronbichler et al., 2012; Heister et al., 2017).We compare the ASPECT results with calculations from the finite-element code CitcomS (Zhong et al., 2000; Tan et al., 2006; Zhong et al., 2008), which has a long history of use in the geodynamics community.We find that the globally averaged quantities, i.e., root-mean-square (rms) velocity, mean temperature, and Nusselt number at the top and bottom of the shell, agree to within 1 % (and often much better) for calculations with sufficient mesh resolution.We also show that there is excellent agreement of the time evolution of both the rms velocity and the Nusselt numbers between the two codes for otherwise identical parameters.Based on our results, we are optimistic that similar agreement would be achieved for calculations performed at the convective vigor expected for Earth, Venus, and Mars.