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Motivation In the pursuit of higher resolution simulation models that use all seismic, geological, and dynamic reservoir data and to make use of modern parallel computing architectures we consider alternative numerical methods to solve the system of equations governing subsurface porous media flow. It is standard in conventional techniques to use a global linearization in a Newton-type method to solve the strongly nonlinear system of equations arising from the spatial and temporal discretization of the governing system of PDEs. Consequently, the memory requirement to store the sparse Jacobian is significant. Such very large linear systems result in the linear solver component to constitute more than 70% of the computation time in reservoir simulators. Iterative linear solvers depend on effective preconditioners, which can be hard to parallelize to the extent required by many-core simulations. In a first step, we investigate feasibility of using the locally linearizing nonlinear multigrid method Full Approximation Scheme (FAS) in serial to establish algorithmic performance.