  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.
