Numerical approach to problems of gravitational instability of geostructures with advected material boundaries

Abstract

We present a numerical approach for solving 2-D mantle flow problems where the chemical composition changes abruptly across intermediate boundaries. The method combines a Galerkin-spline technique with a method of integration over regions bounded by advected interfaces to represent discontinuous variations of material parameters. It allows direct approximation of a natural free surface position, instead of a posteriori calculation of topography from the normal stress at the upper free-slip boundary. We formulate a model where a viscous incompressible fluid filling a square box is divided into layers (not necessarily horizontal) by advected boundaries, across which the density and viscosity change discontinuously. No-slip or free-slip conditions are assumed at the model sides. The suggested approach, being Eulerian, avoids the difficulties due to material discontinuities at intermediate boundaries, like the Moho or the Earth's surface, and is also free from the deficiencies of the Lagrangian approach, always resulting in mesh distortion. We present two geophysical cases analysed by this technique. The first case concerns the formation of sedimentary basins under the effects of heavy bodies sinking in the asthenosphere and of load due to sedimentary infills. The second case demonstrates the evolution of salt diapirs and shows how their growth is affected by a laterally inhomogeneous sedimentary layer. This numerical approach is well suited for problems of gravitational instability with discontinuities of density and viscosity across advected boundaries.