Summary Highly detailed geological models, which are primary inputs for reservoir simulators, necessitate a reduction in the number of grid-blocks used in the solution of flow equations. However, preparing a coarse-scale model that can mimic the fine-scale behavior is challenging. Cartesian grids suffer from some shortcomings, such as in adaptation with geological and geometrical features and the grid-orientation effect that motivates the use of unstructured grids. Different methods have been used for this purpose, but none is robust enough. This justifies further research. In this paper, we propose a novel unstructured-grid-generation scheme that uses the vorticity of fluid flow in porous media as the determining parameter for background-grid generation. It entails simulating single-phase flow on the fine grid and obtaining the velocity field and, subsequently, the vorticity map. Vorticity is then used to generate the background grid that plays an essential role in the generation of a desired final coarse grid. At this stage, users need to determine the value of some parameters, such as maximum and minimum spacing, vorticity cutoff, and vorticity-intensity degree. The advancing-front method and Delaunay triangulation are then used to provide the triangular and Voronoi perpendicular-bisector (PEBI) grid. The developed technique, which aims to capture both flow and geologic details, produces grids with higher resolutions at critical vorticity areas, such as around layer boundaries, and with lower resolution where vorticity is negligible, such as in homogeneous regions. This technique is applied to two channelized and heterogeneous models, and the results are presented. Two-phase-flow simulations are performed on the generated coarse grids, and the results are compared with those of fine-scale grid and uniformly generated coarse grids. The results show a greater accuracy compared with uniformly gridded models.