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Single‐degree of freedom Hermite collocation for multiphase flow and transport in porous media

The classical collocation method using Hermite polynomials is computationally expensive as the dimensionality of the problem increases. Because of the use of a C1‐continuous basis, the method generates two, four and eight unknowns per node for one, two and three‐dimensional problems, respectively. In this paper we propose a numerical strategy to reduce the nodal unknowns to a single degree of freedom at each node. The reduction of the unknowns is due to the use of Lagrangian polynomials to approximate the first‐order derivatives over the minimal compact stencil surrounding each node. For the solvability of the problem the reduction of the number of collocation equations is done by a nodal weighting strategy. We have applied the proposed approach to enhance the efficiency of a collocation‐based multiphase flow and transport simulator. Benchmark cases illustrate the higher performance of the new methodology when compared to classical Hermite collocation. Copyright © 2004 John Wiley & Sons, Ltd.