In this paper a time-splitting approach for the advection-dispersion equation describing solute transport in two dimensional porous media is proposed. A triangle-based high resolution Finite Volume (FV) scheme for advection is combined with RT0 Mixed Hybrid Finite Element (MHFE) technique for dispersion. Second order in time is achieved by employing the midpoint rule for FV and Crank-Nicolson for MHFE, and by adding a diffusion-dependent term in the advective step. This term, calculated by Taylor expansion in the linear reconstruction phase, is needed to restore second order accuracy, that is lost because of the time-splitting approach. Numerical tests on an analytical 1-dimensional example ascertain the properties of the scheme.
Triangular finite volume-mixed finite element discretization for the advection-diffusion equation
MAZZIA, ANNAMARIA;BERGAMASCHI, LUCA;PUTTI, MARIO
2000
Abstract
In this paper a time-splitting approach for the advection-dispersion equation describing solute transport in two dimensional porous media is proposed. A triangle-based high resolution Finite Volume (FV) scheme for advection is combined with RT0 Mixed Hybrid Finite Element (MHFE) technique for dispersion. Second order in time is achieved by employing the midpoint rule for FV and Crank-Nicolson for MHFE, and by adding a diffusion-dependent term in the advective step. This term, calculated by Taylor expansion in the linear reconstruction phase, is needed to restore second order accuracy, that is lost because of the time-splitting approach. Numerical tests on an analytical 1-dimensional example ascertain the properties of the scheme.
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