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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.

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