A Lagrangian‐Eulerian Method with zoomable hidden fine‐mesh approach to solving advection‐dispersion equations

A Lagrangian‐Eulerian method with zoomable hidden fine‐mesh approach (LEZOOM), that can be adapted with either finite element or finite difference methods, is used to solve the advection dispersion equation. The approach is based on automatic adaptation of zooming a hidden fine mesh in regions where the sharp front is located. Application of LEZOOM to four bench mark problems indicates that it can handle the advection‐dispersion/diffusion problems with mesh Peclet numbers ranging from 0 to ∞ and with mesh Courant numbers well in excess of 1. Difficulties that can be resolved with LEZOOM include numerical dispersion, oscillations, the clipping of peaks, and the effect of grid orientation. Nonuniform grid as well as spatial temporally variable flow pose no problems with LEZOOM. Both initial and boundary value problems can be solved accurately with LEZOOM. It is shown that although the mixed Lagrangian‐Eulerian (LE) approach (LEZOOM without zooming) also produces excessive numerical dispersion as the upstream finite element (UFE) method, the LE approach is superior to the UFE method.