No abstract

Seismic imaging of the mantle has revealed large and small scale heterogeneities in the lower mantle; specifically structures known as large low shear velocity provinces (LLSVP) below Africa and the South Pacific. Most interpretations propose that the heterogeneities are compositional in nature, differing in composition from the overlying mantle, an interpretation that would be consistent with chemical geodynamic models. The LLSVP's are thought to be very old, meaning they have persisted throughout much of Earth's history. Numerical modeling of persistent compositional interfaces presents challenges, even to state-of-the-art numerical methodology. For example, some numerical algorithms for advecting the compositional interface cannot maintain a sharp compositional boundary as the fluid migrates and distorts with time dependent fingering due to the numerical diffusion that has been added in order to maintain the upper and lower bounds on the composition variable and the stability of the advection method. In this work we present two new algorithms for maintaining a sharper computational boundary than the advection methods that are currently openly available to the computational mantle convection community; namely, a Discontinuous Galerkin method with a Bound Preserving limiter (DGBP) and a Volume-of-Fluid (VOF) interface tracking algorithm. We compare these two new methods with two approaches commonly used for modeling the advection of two distinct, thermally driven, compositional fields in mantle convection problems; namely, an approach based on a high-order accurate finite element method (FEM) advection algorithm that employs an artificial viscosity technique known as 'Entropy Viscosity' (FEM-EV) to maintain the upper and lower bounds on the composition variable as well as the stability of the advection algorithm and the advection of particles that carry a scalar quantity representing the location of each compositional field. All four of these algorithms are implemented in the open source FEM code ASPECT, which we use to compute the velocity, pressure, and temperature fields associated with the underlying flow field. We compare the performance of these four algorithms by computing the solution to an initially compositionally stratified fluid that is subject to a thermal gradient at a Rayleigh number of Ra = 10 5 with a buoyancy ratio of B = 1.0. For B = 1.0, a value for which the initial stratification of the compositional fields persists indefinitely, our computations demonstrate that the entropy viscosity-based method has far too much numerical diffusion to yield meaningful results. On the other hand, the DGBP method yields good results, although small amounts of each compositional field are numerically entrained within the other compositional field. The particle method yields yet better results than this, but some particles representing the denser fluid are entrained in the upper, less dense fluid and are advected to the top of the computational domain and, similarly, particles representing the less d...

We describe the implementation of a second-order accurate volume-of-fluid interface tracking algorithm in the open source finite element code ASPECT, which is designed to model convection in the Earth's mantle. This involves the solution of the incompressible Stokes equations coupled to an advection diffusion equation for the temperature, a Boussinesq approximation that governs the dependence of the density on the temperature, and an advection equation for a marker indicating the two initial density states. The volume-of-fluid method is fully parallelized and is integrated with the adaptive mesh refinement algorithm in ASPECT. We present the results of several standard interface tracking benchmarks in order to demonstrate the accuracy of the method as well as the results of several benchmarks commonly used in the computational mantle convection community. Finally, we present the results of computations with and without adaptive mesh refinement of a model problem involving thermochemical convection in a computationally stratified fluid designed to provide insight into how thermal plumes, that eventually reach the Earth's surface as ocean island basalts, originate at structures on the core-mantle boundary known as Large Low Shear wave Velocity Provinces.