Multiscale Methods as Spatiotemporal Grid-refinement Techniques

In the last decade, multiscale methods have been developed and proposed to efficiently solve large reservoir models. These techniques allow reducing the computational cost by decreasing the size of the largest problem to be solved: the initial fine-scale problem is divided into a set of independent local problems coupled by a coarse problem which is smaller than the original problem. This approach can be seen as a refined upscaling technique, which uses local numerical solutions to compute coarse parameters and to reconstruct the (approximate) fine-scale details of the solution.