Interpolation techniques applied to the Eulerian-Lagrangian solution of the convection-dispersion equation in natural coordinates

Abstract

A weighted second-order (quadratic) interpolation technique is proposed to eliminate the oscillation phenomena manifested in the numerical Eulerian-Lagrangian solution of the convection-dispersion equation in natural coordinates when sharp fronts of concentration occur. Weighting is based on the interpolation of local moving points by using the known points in the fixed Eulerian grid. To increase numerical accuracy, the use of a third order (cubic) polynomial is discussed. Numerical experiments show that, in comparison with the quadratic formula, the application of this cubic interpolation technique has a number of advantages: (1) numerical oscillation is much less important or disappears; (2) the upstream spatial shift brought about by the quadratic formula disappears; and (3) stability is greater, even when the grid current number is larger than 1. The proposed numerical model is tested against two classical problems for which analytical solutions exist. The additional comparison of the numerical results obtained by the Eulerian-Lagrangian method using cubic interpolation, and those obtained by a purely Eulerian method (UWMCB), is carried out to illustrate the possibility of a real gain in precision.