NUMERICAL TECHNIQUE FOR CALCULATION OF THREE-DIMENSIONAL MANTLE CONVECTION AND TECTONICS OF CONTINENTAL PLATESV. V. Rykov and V. P. Trubitsyn
We present an algorithm for numerical modeling of three-dimensional viscous flows governed by Stokes', continuity, and thermoconvection equations in a rectangular three-dimensional region. We apply the finite-difference technique to these equations written in terms of natural variables, that is, velocity components, pressure, and temperature. At each time step we solve one parabolic and five elliptic equations, one after another. Lithospheric plates are assumed to be thin and perfectly rigid, drifting on the surface of a viscous fluid. The thermomechanical coupling between the flow and the plates is introduced through boundary conditions representing no-slip and zero heat flux conditions at the bottom of the plates. The translatory and rotary motions of the plates depend on the velocity of mantle flows and on mechanical interaction between the plates. We calculated movements of Laurasia and Gondwana supercontinents, including formation and breakup of Pangea. Initially, steady convection is assumed in a three-dimensional rectangular $3\times 3\times 1$ box. The initial positions of the continents are taken from geological reconstruction data for 1 billion years ago. Numerical results show that the continents approach each other and converge into Pangea covering the descending mantle flow. Then the convection pattern changes due to thermal insulation at the boundary. An ascending flow forms in place of the formerly descending flow, which leads to the breakup of Pangea after several hundred million years.