Gerya T.V. «Numerical modelling of iron core formation with finite differences and marker-in cell techniques» Механика, управление и информатика, № 4, с. 7-14 (2011)

Thermo-mechanical numerical modelling becomes more and more popular tool for understanding iron core formation mechanisms during planetary accretion and differentiation. Modelling of iron core formation in a self-consistent manner should take into account realistic rheology of planetary materials and large internal deformation of a self-gravitating planetary body. This requires computing complex visco-(elasto)- plastic deformation in the variable gravity field which changes with time in response to evolution in mass distribution inside the planet. Changes in the shape of the planet and the related planetary surface deformation should also be considered. One way to tackle these requirements is to use the spherical-Cartesian approach that allows computations of self-gravitating bodies of arbitrary form on Cartesian grids including the presence of a free surface. In this paper 2D implementation of this approach based on finite differences and marker-in-cell techniques is discussed in short together with test numerical examples.