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Flux-limiting and nonlinear solution techniques for simulation of transport in porous media. (English) Zbl 1049.76047

Summary: The conservation laws governing the flow of liquids in porous media are often nonlinear and have steep fronts that require resolution in time. It is one of the aims of this work to analyse the use of higher order spatial weighting schemes and temporal methods for reducing numerical dispersion. Another important ingredient in the development of an efficient simulator is the treatment of the nonlinear system that results from the discrete analogue of the conservation law. In this work a vertex-centered finite volume method is used for discretising a representative conservation law in one-dimension and two nonlinear iterative methods, an inexact full Newton method and the modified Shamanskii method, are scrutinised. Two case studies are chosen to highlight the performance of the chosen numerical techniques. At first, the focus is on the accuracy and efficiency of the spatial weighting methods for a linear advection-dispersion equation and then, a two-phase flow problem is analysed to gauge the performance of the non-linear solvers. In both cases, comparisons with exact solutions are presented.

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76S05 Flows in porous media; filtration; seepage
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