Practical finite analytic methods for simulation of advection-dominated solute transport

The practical finite-analytic (PFA) method was applied to the solution of the one-dimensional advection-dispersion equation (ADE) for solute transport in porous media under advection-dominated (high Peclet number, Pe) conditions. Several PFA spatial-temporal computational molecules were developed for Cauchy and pulse loading boundary conditions. The PFA solutions were compared with solutions from the upwind method and quadratic upwind differencing (QUICK) scheme. For all boundary conditions the trapezoidal explicit PFA (EPFA) computational molecule gave the most accurate results at very high Pe number as long as the Courant number (Cr) was close to one. Stability analysis shows that the PFA molecules are always stable for high Pe number. ResumeLa methode analytique finie pratique (AFP) a ete appliquee a la solution de l'equation unidimensionnelle d'advection-dispersion (EAD) pour le transport advectif dominant de solute en milieu poreux (nombre de Peclet (Pe) eleve). Plusieurs methodes de calcul spatio-temporel de l'AFP ont ete developpees pour les conditions aux limites de Cauchy et de charge periodique. Les solutions AFP ont ete comparees avec les solutions de la methode de stabilisation et du du schema stabiise de differenciation quadratique (QUICK). Pour toutes les conditions aux limites, la methode trapezoidale de calcul AFP explicite (AFPE) a donne les resultats les plus precis pour des Pe tres eleves tant que le Courant (Cr) etait proche de un. L'analyse de stabilite montre que les methodes AFP sont toujours stables pour un Pe eleve.