We study linear and nonlinear finite volume methods coupled to the high order methods to simulate the behavior of flows in porous media with complex geological properties. Ideally, the linear and nonlinear methods should satisfy the following numerical properties: Preserve linearity, handle full and discontinuous tensors, satisfy the discrete maximum principle, or at least preserve monotonicity. On the other hand, we are interested in proposing higher order methods capable of avoiding undesirable oscillations near discontinuities, reducing the grid orientation effect, and avoiding excessive numerical diffusion using limiter functions multidimensional. In addition, the proposed methods must be able to deal with unstructured and/or distorted meshes.