Implementation of a Volume-of-Fluid Method in a Finite Element Code with Applications to Thermochemical Convection in a Density Stratified Fluid in the Earth's Mantle

TL;DR

This paper details the implementation of a second-order volume-of-fluid interface tracking algorithm within the ASPECT finite element code, applied to mantle convection modeling, demonstrating accuracy and efficiency through benchmarks and geophysical simulations.

Contribution

The authors integrated a second-order volume-of-fluid method into ASPECT with parallelization and adaptive mesh refinement, enabling accurate mantle convection simulations with thermochemical interfaces.

Findings

The method achieves high accuracy in interface tracking benchmarks.

Adaptive mesh refinement improves computational efficiency.

Simulations provide insights into mantle plume formation and surface volcanism.

Abstract

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.