Monotonic solution of flow and transport problems in heterogeneous media using Delaunay unstructured triangular meshes

Transport problems occurring in porous media and including convection, diffusion and chemical reactions, can be well represented by systems of Partial Differential Equations. In this paper, a numerical procedure is proposed for the fast and robust solution of flow and transport problems in 2D heterogeneous saturated media. The governing equations are spatially discretized with unstructured triangular meshes that must satisfy the Delaunay condition. The solution of the flow problem is split from the solution of the transport problem and it is obtained with an approach similar to the Mixed Hybrid Finite Elements method, that always guarantees the M-property of the resulting linear system. The transport problem is solved applying a prediction/correction procedure. The prediction step analytically solves the convective/reactive components in the context of a MAST Finite Volume scheme. The correction step computes the anisotropic diffusive components in the context of a recently proposed Finite Elements scheme. Massa balance is locally and globally satisfied in all the solution steps. Convergence order and computational costs are investigated and model results are compared with literature ones.

► We present a monotonic solution for heterogeneous flow and transport problems.
► Both flux and transport treatment requires Delaunay triangulation.
► Delaunay condition attained using edge-swap without changing nodes location.
► Mass is locally and globally preserved.
► Model is robust with respect to permeability or diffusive tensor abrupt changes.