A recursive algorithm for connectivity analysis in a grid; application to 2D hydrodynamic modeling in heterogeneous soils

A prerequisite for numerical simulation of water flow in heterogeneous soils is to build a discrete model of the soil matrix that is a fair representation of the heterogeneities under study, while being compatible with the numerical equations used to compute unsaturated water flow. When introducing significant amounts of very coarse solid elements (gravels) in a discrete, multi-dimensional soil matrix model, in the form of internal boundaries that occupy a certain fraction of the grid nodes, the need arises to eliminate from the model the possible occurrence of isolated areas of soil, surrounded by continuous gravel barriers that keep them separate from other regular grid nodes. This situation is obviously an artefact resulting from the discrete representation of the physical system, since all nongravel areas ought to be considered as being submitted to at least some hydrodynamic linkage with each other and with the outer boundary conditions (rain and other water input at the top, gravity drainage or water table at the bottom). Computational nodes that do not connect in some way, through the computational grid, to these outer boundary conditions, are the source of computational problems due to system indetermination when solving the hydrodynamic equations. A method has thus been devised to automatically detect and eliminate such situations in order to produce plausible soil models for hydrodynamic simulation, in the presence of highly contrasted grain sizes. The method is based on a proposed recursive algorithm for cluster analysis, an attractive and very simple alternative to existing methods generally used to handle cluster problems. This method and its application to the heterogeneous soil modeling problem is presented as a pseudo-code that can be implemented with any current programming language. Performance figures, and simulation results of the hydrodynamic behavior of such soil models, are shown. A parallel implementation of the algorithm is also proposed. (C) 2000 Elsevier Science Ltd. All rights reserved.