A Time-Splitting Technique for the Advection-Dispersion Equation in Groundwater

Abstract

In this paper a time-splitting technique for the two dimensional advectiondispersion equation is proposed. A high resolution in space Godunov method for advection is combined with the RT0 Mixed Finite Element for the discretization of the dispersion term. Numerical tests on an analytical one dimensional example ascertain the convergence properties of the scheme. At di erent Peclet numbers, the choice of optimal time step size used for the two equations is discussed, showing that with accurate selection of the time step sizes, the overall CPU time required by the simulations can be drastically reduced. Results on a realistic test case of groundwater contaminant transport con rm that the proposed scheme does not su er from Peclet limitations, and always displays only small amounts of numerical di usion across the entire range of Peclet numbers.

Solving the advection–diffusion equation on unstructured meshes with discontinuous/mixed finite elements and a local time stepping procedure

“…This approach, where several advective time steps are computed before taking a single diffusion time step, yields considerable CPU savings, if compared with the case with M = 1, where both time steps are equal [3,19,20].…”

“…Advection and diffusion are then solved using different numerical techniques that are specifically suited to achieve high accuracy for each type of equation [17][18][19]. In the literature, several authors [3,20] combined the DG method for advection with the mixed finite element method for diffusion.…”

The MAST FV/FE scheme for the simulation of two-dimensional thermohaline processes in variable-density saturated porous media

“…The second one indicates the ratio between the advective and the diffusive term and is defined as (see for example [37]):…”

“…For the advective components of the transport equation some authors (see for example [37][38][39]) adopt high resolution triangular finite volume (FV) discretization, combined with an implicit mixed hybrid finite element (MHFE) scheme for the solution of the flow equation and of the diffusive components in the transport equation. MHFE methods compute a velocity field which is very good for the solution of the next convective transport problem with the FV methods, since the normal velocity components are continuous across the inter-element boundaries.…”

Comparison of 3D Flow Fields Arising in Mixed and Standard Unstructured Finite Elements

“…It is known that the Galerkin approach on tetrahedrons may lead to numerical inaccurate and not mass-conserving fluxes, in particular for heterogeneous conductivity tensors [1,2,3]. The MHFE formulation that we exploited is an extension to 3D tetrahedral meshes of a 2D algorithm for triangular meshes [4,5]. The pressure ψ, the Lagrange multipliers λ, and the flux v are approximated by…”