Abstract
A fractal mobile-immobile (MIM in short) model for solute transport in heterogeneous porous media is investigated from numerics. An implicit finite difference scheme is set forth for solving the coupled system, and stability and convergence of the scheme are proved based on the estimate of the spectral radius of the coefficient matrix. Numerical simulations with different parameters are presented to reveal the solute transport behaviors in the fractal case.
Highlights
IntroductionSolute transport in porous media is a complicated process involving in physical/chemical and biological reactions with fluid mechanics, and the traditional models are the advection-dispersion equations and the MIM solute transport models
Solute transport in porous media is a complicated process involving in physical/chemical and biological reactions with fluid mechanics, and the traditional models are the advection-dispersion equations and the MIM solute transport models.The MIM model describes the hydrodynamic behavior in the mobile zone and the mass transfer process between the mobile zone and the immobile zone, which can characterize the physical/chemical non-equilibrium of solute transport in heterogeneous porous media
By discretizing the fractional derivatives and integer-order derivatives in (1.2), an implicit finite difference scheme is established, and the unconditional stability and convergence of the scheme are proved by estimating the spectral radius of the coefficient matrix under natural conditions, and numerical simulations are performed with different parameters to reveal the subdiffusion behaviors of the solute in fractal cases
Summary
Solute transport in porous media is a complicated process involving in physical/chemical and biological reactions with fluid mechanics, and the traditional models are the advection-dispersion equations and the MIM solute transport models. The MIM model describes the hydrodynamic behavior in the mobile zone and the mass transfer process between the mobile zone and the immobile zone, which can characterize the physical/chemical non-equilibrium of solute transport in heterogeneous porous media. (0, 1) × (0, T ); R1, R2 ≥ 1 are the retardation factors, λ, μ > 0 are the degradation coefficients in the mobile and immobile respectively; and P > 0 denotes the Pelect number, β ∈ (0, 1) the partitioning coefficient, and ω > 0 the mass transfer rate. By discretizing the fractional derivatives and integer-order derivatives in (1.2), an implicit finite difference scheme is established, and the unconditional stability and convergence of the scheme are proved by estimating the spectral radius of the coefficient matrix under natural conditions, and numerical simulations are performed with different parameters to reveal the subdiffusion behaviors of the solute in fractal cases.
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