Example embodiments utilize machines to model reservoir geometry having geological layers as 2.5D unstructured grids. Example embodiments include program products to simulate a reservoir by generating a reservoir data system, performing a numerical fluid flow simulation, and visualizing the simulation. Data system embodiments include data structures to model a reservoir geometry as laterally unstructured two-dimensional (2D) grids and associated layer depths defining z-lines to thereby define a 2.5D unstructured grid, including datasets for: vertices of the grid cells for the future grid top and bottom surfaces, a number and listing of vertices for each grid cell, cell center coordinates, and vertex adjacency information using a compressed sparse row format. Computer-implemented methods include projecting external and internal boundaries onto a future grid surface; generating 2D unstructured, e.g., Voronoi, grids, for the top and bottom surfaces; and generating z-lines of depths corresponding to reservoir layers to thereby generate 2.5D unstructured grids.