A Two-Stage Operator Splitting Algorithm for the Numerical Simulation of Contaminant Transport in Unsaturated Porous Media J. Aquino 1 *, A. S. Francisco 2 , F. Pereira 3 , and H. P. Amaral Souto 1 1 Departamento de Modelagem Computacional, Instituto Politécnico, Universidade do Estado do Rio de Janeiro, Caixa Postal 97282, 28601-970 Nova Friburgo, RJ, Brazil {jaquino,helio}@iprj.uerj.br 2 Departamento de Ciência dos Materiais, Escola de Engenharia Industrial Metalurgica de Volta Redonda, Universidade Federal Fluminense, Av. dos Trabalhadores, 420, 27255-250 Volta Redonda, RJ, Brazil afrancisco@metal.eeimvr.uff.br 3 Department of Mathematics and School of Energy Resources, University of Wyoming, Laramie, WY 82071-3036, U.S.A. felipepereira62@gmail.com Abstract. In this paper we introduce a two-stage operator splitting algorithm for the numeri- cal simulation of contaminant transport in unsaturated, heterogeneous porous media. This problem is modeled by a system of equations that describes two-phase water-air flow and contaminant transport within the water phase. The splitting scheme aims at accuracy and computational efficiency. It allows us to combine Eulerian (for the nonlinear water-air prob- lem) and Lagrangian (for the linear transport equation associated with contaminant transport) numerical methods in the solution of the governing system of equations. The water-air flow equations are approximated by mixed finite elements (for the pressure-velocity problem) combined with a second-order, non-oscillatory central finite difference scheme (for the water saturation equation). For the numerical approximation of the advective transport of the con- * Corresponding Author. Email: jaquino@iprj.uerj.br. International Journal of Computational Science 1992-6669 (Print) 1992-6677 (Online) www.gip.hk/ijcs © 2008 Global Information Publisher (H.K) Co., Ltd. All rights reserved. A Two-Stage Operator Splitting Algorithm 1 GLOBAL INFORMATION PUBLISHER