Migration of pollutants in groundwater. III. Numerical dispersion reduction with cartesian coordinates

The partial differential equation governing the movement of a decomposing pollutant undergoing 2-dimensional flow in a saturated aquifer is examined. The analytical solution of the equation is usually not possible, and use of mesh numerical integration techniques causes excessive numerical dispersion to arise from the advection term. We apply two asymmetrical upwind formulas to approximate the advection term. These markedly reduce numerical dispersion without requiring the use of coordinate systems obtained by conformal mapping. Flow within a right angle and flow toward a sink in an otherwise uniform field are analyzed to illustrate the methods.