Modified Eulerian Lagrangian Method for Flow and Transport in Heterogeneous Aquifers

Abstract

A Modified Enlerian La.grangia.n (MEL) method is developed for the numerical solution of flow and transport in a heterogeneous aquifer. This is emerging from Lagrangian formulation of the governing equations written in terms of reduced velocities associated with the material derivatives. These velocities,for forward and backward particle tracking techniques, depend on the heterogeneity of various solid matrix and fluid properties. Particles,in the transport problem, are shifted by a combination of fluid’s velocity and the gradient of the hydrodynamic dispersion. In time case of the flow problem. we apply the MEL scheme with particle’s velocity associated with the gradient of hydraulic conductivity.

Comparisons between the MEL, the Eulerian Lagrangiau (EL) and the Eulerian Finite Elements (EFE) methods prove that the MEL scheme is superior in yielding almost no deviations from analytical solutions of I-D flow and transport in a saturated aquifer.

Evolution of spatial accumulation of numerical mass balance errors, prove that such an assessment. may be misleading.

The vertical unsaturated/saturated flow a.nd transport problem is formulated by the MEL method as an example demonstrating the parabolic transformation of the governing equations.