Abstract: A method modeling a physical process in a material environment. A system of modeling equations at the level of each of the grid cells of a grid pattern involves a number n of cells subdividing the environment. The model is achieved at a relatively low cost and within a reasonable calculating time in relation to the quality and the accuracy of the simulations obtained, mainly by reducing the size of the solution problem. To that effect, a Krylov space of dimension d, much smaller than the number n of grid cells, is used. This has the effect of reducing the volume of the solution operations. The method can be used for modeling of fluid flow in an underground reservoir of, for example, hydrocarbons.