Solution of the advective-dispersive transport equation using a least squares collocation,Eulerian-Lagrangian method

Numerical solution of the advective-dispersive transport equation is difficult when advection dominates. Difficulties arise because of the first-order spatial derivatives which can be elminated by a local coordinate transformation to the characteristic lines of the first order hyperbolic portion of the equation. The resulting differential equation is discretized using a finite difference in time and finite elements in space employing cubic Hermite basis functions. The residuals at individual collocation points are then computed. The sum of the squares of the residuals is minimized to form the necessary set of algebraic equations. The method has performed well in one-dimensional test problems.