black oil formulation for the multiscale finite volume method

until now, the multiscale finite volume (msfv) method has shown great promise in petroleum subsurface flow simulation when applied to large and highly heterogeneous reservoirs. recently, the method was extended from incompressible multiphase flow to a standard black oil formulation, i.e., compressible rock/fluid system with gravity and solution gas. the new formulation requires modified basis functions and handles upstream consistently in pressure and transport calculations. in our approach we split the governing operator is into an incompressible, a compressible and a gravity contribution to handle the physics correctly on fine and coarse scale. we detail the formulation and assess the accuracy of the new method with numerical examples relative to detailed fine grid simulations. keywords multiscale, finite volume, subsurface, black oil