We have devised a numerical tool for studying processes that take place in the deeper mantle, using MILAMINs fast MATLAB-based Stokes and thermal solvers.
A thermomechanical Finite Element Method (FEM) code is developed to model convection of a viscous fluid in a rectangular domain. The fluid is confined in an impermeable box and is heated from below, with no internal heating. It is assumed that the fluid is of infinite Prandtl number, with Newtonian rheology and that the Boussinesq approximation applies. The fluid is comprised by two chemically distinct materials: a dense layer along the bottom boundary overlain by a material of lower density and higher viscosity. Density and viscosity of the entire fluid are both temperature- and chemistry-dependent. Mechanical boundary conditions are free slip on all four sides of the box. Thermal boundary conditions are isotherms on top and bottom boundaries and zero heat flux on lateral boundaries.
The governing equations include the conservation laws of mass, energy, and momentum, as well as the thermal and chemical dependence of viscosity. Density variations are expressed as a linear combination of thermal and chemical contributions.
Two independent grids are used for spatial discretization of the temperature and velocity fields. We use a structured grid, and the resolution is determined by the number of mechanical elements in vertical direction and the number of thermal elements per mechanical element. Different materials in the model are represented by markers, and material transport associated with convection is modeled using marker-in-cell technique.
Temporal evolution of the temperature field and distribution of the dense layer are presented below. The resolution is determined by 100 mechanical elements in vertical direction and 2×2 thermal elements per mechanical element. We use second order quadratic elements for the velocity, and first order quadratic elements for the temperature.