Journal of Conference Abstracts

3D Finite-element Modelling of Viscous Flow: Application to the Evolution of Salt Structures

Alik Ismail-Zadeh (aismail@mitp.rssi.ru)¹, Igor Tsepelev (tsep@odu.imm.intec.ru)², Christopher Talbot (talbot@sparc.geo.uu.se)³ & Per Öster (per@pdc.kth.se)⁴

¹International Institute of Earthquake Prediction Theory, Russ. Acad. Sc., Warshavskoye sh. 79, kor.2, Moscow, 113556, Russia

²Institute of Mathematics and Mechanics, S.Uralian Branch, Russ. Acad. Sc., S. Kovalevskaya ul. 16, Ekaterinburg, 620219, Russia

³Institute of Earth Sciences, Uppsala University, Villavagen 16, Uppsala, SE-752 36, Sweden

⁴Center for Parallel Computers, Royal Institute of Technology, Stockholm, SE-100 44, Sweden

We present a numerical approach for computing three-dimensional viscous flows, which can be useful for the analysis of deformations in sedimentary basins containing a salt layer. We employ an Eulerian finite-element model introducing a vector potential for velocity of incompressible flows and representing it as a linear combination of tricubic splines with unknown coefficients. The variable density and viscosity are represented in the same manner. The unknown coefficients in spline representations of density and viscosity are found from sets of ordinary differential equations following from transfer equations for these variables. The coefficients in spline representations of vector potential entering the right-hand sides of these sets are found from the set of linear algebraic equations following from Stokes equations. We develop parallel algorithms and numerical codes to solve the problem. The performance of the codes is compared between two parallel computers, Russian transputer and IBM SP2. There is also a comparison of these computers with respect to a single node performance. We demonstrate the method presenting a case where a salt layer raises in denser surrounding material and induces a flow resulting in the formation of salt-pillow, -diapirs and -walls, successively. The numerical technique can be applied to problems of Rayleigh-Taylor instability.