# Modified Eulerian Lagrangian Method for Flow and Transport in Heterogeneous Aquifers

• S. Sorek
• S. Lumelsky
Part of the International Centre for Mechanical Sciences book series (CISM, volume 364)

## 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.

## Keywords

Distance Figure Transport Problem Numerical Dispersion Heterogeneous Aquifer Maximum Absolute Deviation
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## References

1. [1]
Neuman, S. P. A Eulerian-Lagrangian numerical scheme for the dispersion-convection equation using conjugate space-time grids,.1. Comp. Phys., 41 (2), 270–294, 1981.
2. [2]
Neuman, S. P. Adaptive Eulerian–Lagrangian finite element method for advection–dispersion, Int. J. Num. Math. Eng., 20, 321–337, 1984.
3. [3]
Neuman, S. P. and Sorek, S. Eulerian-Lagrangian methods for advection - dispersion, Proc. 4-th Int. Conf. F. E. W. R., Germany, 1441–1468, 1982.Google Scholar
4. [4]
Sorek, S. and Braester, C. Eulerian-Lagrangian formulation of the equations for groundwater denitrification using bacterial activity. Adv. W. Resour., 11 (4), 162–169. 1988.Google Scholar
5. [5]
Sorek. S. Eulerian-Lagrangian formulation for flow in soil. Adv. W. Resour., 8, 118–120. 1985a.
6. [6]
Sorek, S. Adaptive Eulerian-Lagrangian method for transport problems in soils, Scientific Basis for Water Water Resources Management, IASII Publication, 153, 393–103, 1985b.Google Scholar
7. [7]
Sorek. S. Eulerian-Lagrangian method for solving transport in aquifers, Adv. W. Resour., 11 (2), 67–73, 1988.
8. [8]
Bentley, L. R. and Pinder, G. F. Eulerian-Lagrangian solution of the vertically averaged groundwater transport equations, W. Resour. Res., 28 (11), 3011–3020, 1992.
9. [9]
Baptista, A. E. Solution of advection dominated transport by Eulerian-Lagrangian method, using the backward method of characteristics, Ph.D. Dis., MIT, 1987.Google Scholar
10. [10]
Allen, M. B. and Khosravani, A. Eulerian-Lagrangian method for finite-element collocation using the modified method of characteristic, Computational, Methods in Subsurface Hydrology Proc 8 Int. Conf. Comput. Method Water R.esour, Springer-Verlag Publishers, Berlin, 375–379, 1990.Google Scholar