A 3D unstructured triangular numerical algorithm for simultaneous effects of fluid density variation and water table gradient in saturated porous media

Abstract

A fully three dimensional hydrodynamic implicit numerical algorithm has been proposed for simultaneous simulation of fluid density variation and water table gradient in saturated porous media. Unlike the most of the performed researches that primarily restricted to solute transport simulation in confined or unconfined aquifers without proceeding to forecast water table transient situation, the proposed model can truly handle corresponding problems in an unconfined aquifer having sharp water table gradient. The algorithm is based upon a staggered finite volume scheme on an unstructured triangular mesh in the plane and structured grid in vertical that solves the most general form of Darcy equation without limiting assumptions, not expressed as a function of the groundwater potential but presented in term of the water pressure. Avoiding the excessive computational efforts, an efficient and simple algorithm has been proposed to discretize flow equations, track the water table position and determine salinity distribution. A line iterative method has been utilized efficiently, in a way that, resultant linear equations system splits into a series of tri-diagonal square matrix systems whereby the direct together with iterative procedure employed simultaneously to achieve problem unknowns. Prediction of passive scalar salinity quantity has been achieved efficiently by employing the advantageous time splitting algorithm. This has allowed designing and applying different numerical schemes more compatible with the mathematical and physical properties of the corresponding phenomena. Performance of the 3D model has been validated against a range of problems. Comparison between numerical results, analytical solutions, and experimental data demonstrates that the model represents well the simultaneous effects of fluid density variation and water table gradient processes.