A Direct Substitution Method for Multicomponent Solute Transport in Ground Water

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Abstract
A numerical method was developed using a direct substitution approach for simulating one‐dimensional multicomponent solute transport in ground water. The method has the ability to treat equilibrium reactions of aqueous and surface complexation, and precipitation‐dissolution. The concentrations of aqueous component species, adsorbed component species, and precipitated species are chosen as the principal dependent variables. The substitution takes place after the transport equation is discretized. The resulting system of equations is solved using the Newton‐Raphson method and the Jacobian matrix is computed analytically. This method is computationally more efficient than sequential iteration methods due to its faster convergence rate. It is also computationally more efficient than other direct substitution methods which compute the Jacobian matrix numerically.