Numerical benchmark study for the finite element computer code NEPTUNE

NEPTUNE is a finite element computer code developed for the Subseabed Disposal Program to provide calculations of long-term sediment deformation and pore fluid flow. A benchmark study has been completed as part of the code verification process. The study is based on calculations of free convection in a rectangular region with an end-to-end temperature difference. Two limiting cases are considered, one approximating Darcy flow in a rigid porous medium, and the other approaching the flow of a single-phase, linearly viscous fluid. Results from these calculations are compared to independent results using the more specialized, but thoroughly tested, codes MARIAH and NACHOS. Comparisons of velocity and temperature fields are excellent, with noticeable discrepancies only at Rayleigh numbers several orders of magnitude greater than those expected in a typical subseabed disposal scenario. The calculations are extended successfully into a realm in which both convection of the skeleton and relative motion of the pore fluid contribute significantly to the heat transfer.