The Multiscale Finite Volume Method: A flexible tool to model physically complex flow in porous media
Ivan Lunati, Patrick Jenny · Infoscience (Ecole Polytechnique Fédérale de Lausanne) · 2006
The Multiscale Finite-Volume (MSFV) method has been developed to solve homogeneous elliptic equation on large and highly heterogeneous domains efficiently and has been applied to multiphase flow problems. It employs an auxiliary coarse grid, together with its dual, to define and solve a coarse-scale pressure problem. A set of basis functions, which are local solutions on dual cells, is used to interpolate the coarse-grid pressure and obtain an approximate fine-scale pressure distribution. Then, by solving a set of local problems on coarse cells, a conservative flux field is constructed. The MSFV method has been modified to provide a tool that can model complex physical processes. In this case, the pressure equation might include a source term (which may arise due to gravity or capillary forces) and the basis functions are not good interpolators. An accurate fine-scale pressure can be computed by adding a correction function to the basis-function interpolated pressure. In this framework, the effects of physically complex processes are exclusively described by the correction function and are included in the conservative flux field by solving local problems including the full physics. In future we plan to apply a similar strategy to improve the ability of the MSFV method to solve nonlinear pressure equations as in the case of highly compressible flow. 10th European Conference on the Mathematics of Oil Recovery — Amsterdam, The Netherlands, 4 – 7 September 2006