A dynamically adaptive Godunov scheme for reservoir simulation on large aspect ratio grids

Abstract

Abstract 1 Introduction Large aspect ratio grids are commonly used in the simulation of a vertical cross section of a reservoir, where height is much smaller than length. Unit aspect ratio grids are typical for areal simulations. The combination of a higher order Godunov scheme with dynamic grid adaptivity applied to reservoir simulation is significantly faster than the standard simulator scheme (first order upwind on a uniform grid) while producing far superior results for areal problems (Edwards 1992). The results obtained from applying the adaptive higher order Godunov scheme to a vertical cross section using a grid with cells of large aspect ratio show a deterioration in accuracy as the aspect ratio is increased. Large local errors appear in the solution at grid interfaces which separate cells of different levels.