Current flow-simulation meshes of natural oil reservoirs (NOR) are composed of hundreds of thousands of hexahedral cells. The visualization of the geometry of these cells superimposed with color attributes to represent properties and flow results requires the rendering of an unstructured mesh of millions of triangles. Current graphics hardware does not allow for an interactive visualization of such meshes. As computers and graphics boards increase their processing capacity, simulation meshes also grow and the solution to the rendering problem usually includes acceleration techniques, one of which is multi-resolution (MR). However, currently known MR models are not applicable to NOR simulation meshes due to this field`s specific requirements, such as the preservation of the hexahedral- cell model and discontinuities among cells. In fact, MR techniques tend to focus on Realistic Visualization, while the NOR problem is one of Scientific Visualization, for which generic solutions still do not exist. The present work proposes a specific MR model for the visualization problem concerning NOR simulation meshes, in which discontinuous space partition, hexahedral-cell-based semantics and the problem`s visualization characteristics are taken into account. The proposed model allows an efficient construction of a MR structure, from which, in real time, adaptive meshes can be extracted that depend on: (a) the geometric error approximation, (b) the view, and (c) the polygon budget. This model can also be used combined with another acceleration technique, frustum culling, which allows for the hierarchical elimination of regions in the mesh that are out of the view volume. The proposed model was implemented in a system on which extensive testing was performed, providing results that allowed us to draw some conclusions and recommendations.