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Least square-based finite volumes for solving the advection-diffusion of contaminants in porous media. (English) Zbl 1086.76045
Summary: A second-order cell-centered finite volume method is proposed to solve the steady advection-diffusion equation for contaminant transport in porous media. This method is based on a linear least square reconstruction that maintains the approximate cell-average values. The reconstruction is combined with an appropriate slope limiter to prevent the formation of spurious oscillations in the convection-dominated case. The theoretical convergence rate is investigated on a boundary layer problem, and the preliminar results show that the method is promising in the numerical simulation of more complex groundwater flow problems.

76M12 Finite volume methods applied to problems in fluid mechanics
76S05 Flows in porous media; filtration; seepage
76R99 Diffusion and convection
Full Text: DOI
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