The dissertation presents a new gridding concept for hydrocarbon reservoir modeling. The developed algorithms and implementations aim at improving the modeling of complex geological features, the correct representation of the fluid flow within the reservoir, the calculation of near-well behavior, the handling of the full range of simulation problems, and minimizing the turn-around time of the simulation work. The concept is based on the Control Volume Finite Difference (CVFD) method using Two Point Flux Approximation (TPFA) applied on anisotropic domains and leads to the so-called k-orthogonal Perpendicular Bisection or KPEBI grids. The work shows that correct two point flux approximation (TPFA) is always possible for anisotropic permeability domains represented by a permeability tensor if the grid points can be distributed in a way that the grid points are placed along, or close to the main permeability directions. Using Cartesian grids the principal permeability directions can be restricted to the coordinate lines and the diagonal direction to construct KPEBI blocks without any restriction regarding the anisotropy ratio.