Three-dimensional modeling of salt diapirism: A numerical approach and algorithm of parallel calculations
We present a numerical approach and parallel algorithm for computing three-dimensional viscous ows, which can be useful for the analysis of salt movements in sedimentary basins. We employ the Galerkin method and represent a vector potential for the velocity of incompressible viscous ows as a linear combination of tricubic splines with unknown coeffcients. Density and viscosity are represented as linear combinations of trilinear functions with unknown coeffcients. The unknown coeffcients in the representations of density and viscosity are found from sets of ordinary differential equations following from the equation for advection of these variables. The coeffcients in spline representations of vector potential entering their right-hand sides are found from the linear algebraic equations following from the Stokes equations. We suggest a parallel algorithm for solving relevant systems of linear algebraic and ordinary differential equations. A performance of these algorithm is analyzed. The numerical method and parallel algorithm are designed to model salt diapirism. We simulate the growth of salt diapirs in a sedimentary overburden that was present prior to the movement. Two models of evolution of a salt layer from an immature form into mature upbuilt diapiric structures are considered: (1) salt layer at the bottom of the model region overlain by sediments and (2) inclined salt layer between subsalt layer and salt overburden. The model phases of salt diapirism show such typical structures as deep polygonal buoyant ridges, shallow salt-stock canopies, and others.