Zonal Multiscale Finite-Volume framework

In this work, the zonal Multiscale Finite Volume (zMSFV) framework is presented. The framework generalizes previous extensions of the Multiscale Finite Volume (MSFV) method and allows to integrate additional models in a unified way. The new approach is based on splitting the domain of interest into a classical MSFV domain and additional zones. Within each zone, the solution space is spanned by so-called zonal functions. Coupling of the zonal solutions to the surrounding domain is achieved via extended zonal functions. The construction of basis, zonal and extended zonal functions can be performed such that the functions form a partition of unity. The zMSFV framework allows to include the influence of the zonal functions directly in the coarse-scale problem. Similar to previous MSFV method formulations, the zMSFV framework can ensure conservative coarse-scale solutions and allows for the construction of conservative fine-scale solutions. The main features of the zMSFV framework are used to derive robust preconditioners for iterative solutions of high-contrast problems as encountered in subsurface flow and transport simulations. It is shown that the obtained convergence rates are independent of the contrast.