New numerical approaches for modeling thermochemical convection in a compositionally stratified fluid

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. 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 and a Volume-of-Fluid 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 advection algorithm that employs an artificial viscosity technique 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

State-of-the-Art Computational Methodology for Modelling Processes in the Earth's Mantle

This is a poster describing three algorithms or Scientific Software Elements (SSEs) for computing / modelling processes in the Earth's Mantle. These SSEs have been implemented in the open source code ASPECT, which is a carefully parallelized Finite Element code with Adaptive Mesh Refinement (AMR) for modeling problems in the Earth's mantle. Two of these SSEs have never before been implemented in a code for modeling convection in the Earth's mantle, namely (1) a Volume-of-Fluid interface tracking algorithm and (2) a Bound Preserving Discontinuous Galerkin method. We also describe our implementation of an active tracer particle method in ASPECT and present a method for load balancing the combination of AMR and the work done to use the particles in a computation. We present the results of computations of several standard benchmark problems in computational mantle dynamics with these SSEs