A comparison between a direct and a multigrid sparse linear solvers for highly heterogeneous flux computations

Subsurface hydraulic properties are mainly governed by the heterogeneity of the porous medium considered. Our work aims at characterizing the asymptotic dispersion coefficients for highly heterogeneous permeability fields triggered by advection and constant local dispersion-diffusion. We have developed a fully parallel software for simulating flow and transport. We have compared two well-known sparse linear solvers, based respectively on a multifrontal Cholesky factorization and an iterative structured multigrid method. We study the effect of various parameters, mainly the system size, the number of processors and the degree of heterogeneity of the permeability field