SOLUTION OF THE NONLINEAR TRANSPORT-EQUATION USING MODIFIED PICARD ITERATION

The transport and fate of reactive chemicals in groundwater is governe d by equations which are often difficult to solve due to the nonlinear relationship between the solute concentrations for the liquid and sol id phases. The nonlinearity may cause mass balance errors during the n umerical simulation in addition to numerical errors for linear transpo rt system. We have generalized the modified Picard iteration algorithm of Celia et al.(5) for unsaturated flow to solve the nonlinear transp ort equation. Written in a 'mixed-form' formulation, the total solute concentration is expanded in a Taylor series with respect to the solut ion concentration to linearize the transport equation, which is then s olved with a conventional finite element method. Numerical results of this mixed-form algorithm are compared with those obtained with the co ncentration-based scheme using conventional Picard iteration. In gener al, the new solver resulted in negligible mass balance errors (<\10(-8 )\%) and required less computational time than the conventional iterat ion scheme for the test examples, including transport involving highly nonlinear adsorption under steady-state as well as transient flow con ditions. In contrast, mass balance errors resulting from the conventio nal Picard iteration method were higher than 10% for some highly nonli near problems. Application of the modified Picard iteration scheme to solve the nonlinear transport equation may greatly reduce the mass bal ance errors and increase computational efficiency.