Splitting Methods for Geothermal Processes Simulation

A few numerical algorithms for solving the nonstationary heat transfer equation written in terms "temperature - heat flux" are presented. Thereby, a nonstationary two- or three-dimensional parabolic problem in mixed formulation is considered. Space discretization is implemented by the mixed finite element method based on Raviart-Thomas finite elements of lowest order (for vector functions) and piecewise constant elements (for scalar functions). For the vector equation for the mesh heat flux a few splitting schemes are analyzed. Results of numerical experiments for the proposed schemes and Crank-Nicolson scheme are presented. Special attention is given to the comparison of accuracy for different splitting schemes. For the most accurate schemes parallel algorithms are developed. Several application problems concerning thermochronology of certain geological regions are presented.