Special Seminar in Applied Mathematics

The Multiscale Finite Volume (MSFV) Method has been developed for efficient numerical simulations of multiphase flow in highly heterogeneous anisotropic porous media (e.g. oil reservoirs). In this presentation, I will discuss why a multiscale, and particularly the MSFV, method is necessary for large-scale simulations of coupled flow-transport problems. Then the mathematical framework and the systematic error reduction strategies for time-dependent problems with complex physics are presented. Numerical results for many challenging problems, ranging from highly compressible flows to heterogeneous problems with high-conductive long fractures, are presented and discussed. Finally, the recently developed MSFV formulation for compositional simulations is described; and to-date and future challenges in this research field will be discussed.