This is the result of a multiscale simulation using 141 coarse blocks to coarsen a fine grid with 3241 cells. We compute basis functions by locally approximating solution of the pressure equation $\nabla \cdot \vec{v} = q $ where the velocity is a result of the empirical Darcy's law, $\vec{v} = - \nabla p $. The fine grid is a Voronoi diagram of staggered grid points, resulting in a PEBI grid. The grid adapts to wells and faults.

The transport equation is used to find the saturation as time progresses. We have quadratic type relative permeability curves, $k_{rw} = s_w^2$...

Adaptive updating of the basis functions is used to account for changes in fluid mobility. The MsRSB basis functions are straightforward to define for complex grids, and give good results...