Eulerian-Lagrangian solution of the convection-dispersion equation in natural coordinates

Water Resources Research
By: , and 



The vast majority of numerical investigations of transport phenomena use an Eulerian formulation for the convenience that the computational grids are fixed in space. An Eulerian-Lagrangian method (ELM) of solution for the convection-dispersion equation is discussed and analyzed. The ELM uses the Lagrangian concept in an Eulerian computational grid system. The values of the dependent variable off the grid are calculated by interpolation. When a linear interpolation is used, the method is a slight improvement over the upwind difference method. At this level of approximation both the ELM and the upwind difference method suffer from large numerical dispersion. However, if second-order Lagrangian polynomials are used in the interpolation, the ELM is proven to be free of artificial numerical dispersion for the convection-dispersion equation. The concept of the ELM is extended for treatment of anisotropic dispersion in natural coordinates. In this approach the anisotropic properties of dispersion can be conveniently related to the properties of the flow field. Several numerical examples are given to further substantiate the results of the present analysis.

Publication type Article
Publication Subtype Journal Article
Title Eulerian-Lagrangian solution of the convection-dispersion equation in natural coordinates
Series title Water Resources Research
DOI 10.1029/WR020i007p00944
Volume 20
Issue 7
Year Published 1984
Language English
Publisher American Geophysical Union
Contributing office(s) San Francisco Bay-Delta, Pacific Regional Director's Office
Description 9 p.
First page 944
Last page 952
Online Only (Y/N) N
Additional Online Files (Y/N) N
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