Numerical coupled model of creeping flow of multi-phase fluid

Two-dimensional couple numerical model of creeping flow of multi-phase fluid has been developed. The computational domain consists of relatively thick layer of two-phase medium overlaid by a thin multi-layered viscous sheet. There is mass transition at the conjunction boundary between light component of two-phase layer and the bottom layer of viscous sheet. The general system of governing equations consists of the equations of compaction describing the flow in the two-phase layer and the Reynolds equations describing the flow in the sheet. We take into account the layer structure of the sheet and surface processes of erosion and sedimentation as well. We use the additional asymptotic boundary condition to couple different-type hydrodynamic equations without any iterative improvements. That condition reduces significantly computational costs in comparison with the available coupled models. We fulfill numerical modeling of the evolution of the velocity field and layer boundaries. Numerical results reveal different regimes of evolution of velocity field and layer boundaries at short and long times. At least it consists of two stages with typical time scales, namely, a fast evolution at short times changed by slowly (quasistationary) stage at long times. That kind of evolution depends on geometrical and physical parameters of media rather than external causes. Some possible applications in tectonics and geophysics of these model results are outlined. They can be applied to investigate lithosphere thinning beneath large-scale tectonic depressions. Numerical calculations can be applied in geophysics to study the process of accumulation lightened mantle beneath the Earth crust of active transient zone of ocean-continent.