  In this paper, we propose a physics-preserving multiscale method to solve an
immiscible two-phase flow problem, which is modeled as a coupling system
consisting of Darcy's law and mass conservation equations. We use a new
Physics-preserving IMplicit Pressure Explicit Saturation (P-IMPES) scheme in
order to maintain the local conservation of mass for both phases. Besides, this
scheme is unbiased and if the time step is smaller than a certain value, the
saturation of both phases are bounds-preserving. When updating velocity,
MGMsFEM serves as an efficient solver by computing the unknowns on a coarse
grid. We follow the operation splitting techinque to deal with the two-phase
flow. In particular, we use an upwind strategy to iterate the saturation
explicitly and the MGMsFEM is utilized to compute velocity with a decoupled
system on a coarse mesh. To show the efficiency and robustness of the proposed
method, we design a set of interesting experiments. A rigorous analysis is also
included to serve as a theoretical base of the method, which is well verified
by the numerical results. Both simulations and analysis indicate that the
method attains a good balance between accuracy and computation cost.
