A FINITE-ELEMENT FORMULATION IN LAGRANGIAN COORDINATES FOR HEAT AND FLUID-FLOW IN COMPACTING SEDIMENTARY BASINS

This article presents a numerical model of heat and fluid flow in compacting sedimentary basins formulated in Lagrangian co-ordinates. The Lagrangian co-ordinates are the sediment particle positions of the completely compacted basin. A finite element formulation of excess water pressure and temperature in these Lagrangian co-ordinates is presented, in addition to an equivalent formulation in the real co-ordinates. The later formulation is also Lagrangian of nature, since the elements of the grid in the real co-ordinates always frame the same sediment particles. In other words, it is the Lagrangian grid mapped to the real space. This is done in an iterative loop which solves for excess water pressure, and then updates the real co-ordinates of the sediment particles. By comparing the two finite element formulations it is concluded that the one in real space is the simplest, most efficient and most precise. The model is validated by comparison with two dimensionless one-dimensional solutions, one analytical for the linear case, and one numerical for the non-linear case. Both these one-dimensional solutions are obtained on the unit interval, where the moving top boundary caused by continuous sedimentation is incorporated.