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Abstract: The high advanced techniques in parallel computing can be employed for a better understanding of groundwater flow fluids. Generally, the geological media are very heterogeneous and contain complex structures. Decomposing these structures into, approximately, equivalent sub-structures for a load-balancing is a major challenge. This paper proposes and analyses a new algorithm to simulate parallel flow fluid in such complex media. Fully parallel software is developed, and two well-known sparse linear solvers, based respectively on a multifrontal Cholesky factorization and an iterative structured multigrid method, are compared. The mixed finite element (MFE) method is used to discretize Darcy’s equation. Numerical examples are presented to show the efficiency and robustness of the algorithm proposed. [Copyright &y& Elsevier]