A Pointwise Conservative Method for Thermochemical Convection Under the Compressible Anelastic Liquid Approximation

Abstract

Plate tectonics causes continuous differentiation of the Earth's mantle. At mid-oceanic ridges decompression melting forms a basaltic crust on top of a depleted peridotite. Melting at subduction zones helps generate the continental crust and provides further chemical modifications to the subducting crust and mantle. Subduction introduces the newly formed heterogeneity to the deep mantle where it remixes with older subducted materials as well as the likely remnants of early Earth formation, differentiation, and magma ocean solidification (Elkins-Tanton, 2008;Labrosse et al., 2007). Large scale mantle convection associated with plate tectonics also remixes past and newly generated heterogeneities leading to a "marble cake" mantle (Allègre & Turcotte, 1986;van Keken et al., 2014) with its complicated geochemical history expressed in the broad heterogeneity of mid-oceanic ridge and ocean island basalts (Hofmann, 2014;van Keken et al., 2002;Zindler & Hart, 1986), with indications of preservation of heterogeneity caused by very early differentiation of the Earth's mantle (Boyet & Carlson, 2005) even in modern basalts (Horan et al., 2018). The long-term recycling of oceanic crust mixed in with the depleted harzburgite-derived component and ambient mantle is an attractive explanation (Christensen & Hofmann, 1994;Jones et al., 2020) for the bulk of the seismologically observed Large Low Shear Velocity Provinces (LLSVPs: Garnero & McNamara, 2008) at the base of the mantle. However, it is as yet not clear how significant a contribution any primordial heterogeneity has to these LLSVPs (Ballmer et al., 2016;Li et al., 2014) and whether other, potentially more exotic, processes are at play to maintain chemical heterogeneity (Ballmer et al., 2017;Kellogg et al., 1999).To aid in the understanding of the thermal and chemical evolution of the Earth's mantle we can test hypotheses using predictive models of mantle convection driven by thermal and chemical buoyancy forces. This requires numerical methods to reliably model the evolution of temperature and chemistry that are based on the numerical solution of the governing equations following from conservation of momentum, mass, energy, and chemical species. Significant work has relied on the incompressible Boussinesq approximation (e.g.

Benchmarking the accuracy of higher order particle methods in geodynamic models of transient flow

“…Throughout this paper we focus on problems with negligible diffusion (κ c = 0), which represent for example the advection of the chemical composition of rocks, or the size of grains; particle methods for applications with non-negligible diffusivity and reactions have been described elsewhere (Gerya and Yuen, 2003;Sime et al, 2022). Consequently, instead of equation ( 3)…”