Systems, computer-readable media, and methods are described for performing a reservoir simulation by obtaining reservoir data, obtaining simulation parameters, determining partial differential equations based on the simulation parameters, and performing a timestep of the reservoir simulation based on the reservoir data and the partial differential equations by removing an effect of long coherent structures with high contrasts, such as fractures, faults, high and low permeability channels, or shale layers, from the partial differential equations to generate adapted partial differential equations, and performing an algebraic multiscale method on the adapted partial differential equations to generate an approximated solution. The approximated solution can be used in a subsequent timestep of the reservoir simulation.