GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
A stable and accurate convective modelling procedure based on quadratic upstream interpolation
Computer Methods in Applied Mechanics and Engineering - Special edition on the 20th Anniversary
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Multi-scale finite-volume method for elliptic problems in subsurface flow simulation
Journal of Computational Physics
Multiscale finite-volume method for compressible multiphase flow in porous media
Journal of Computational Physics
Journal of Computational Physics
Iterative multiscale finite-volume method
Journal of Computational Physics
Modeling complex wells with the multi-scale finite-volume method
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
An iterative multiscale finite volume algorithm converging to the exact solution
Journal of Computational Physics
Hybrid Multiscale Finite Volume method for two-phase flow in porous media
Journal of Computational Physics
Hi-index | 31.45 |
Accurate modeling of flow instabilities requires computational tools able to deal with several interacting scales, from the scale at which fingers are triggered up to the scale at which their effects need to be described. The Multiscale Finite Volume (MsFV) method offers a framework to couple fine- and coarse-scale features by solving a set of localized problems which are used both to define a coarse-scale problem and to reconstruct the fine-scale details of the flow. The MsFV method can be seen as an upscaling-downscaling technique, which is computationally more efficient than standard discretization schemes and more accurate than traditional upscaling techniques. We show that, although the method has proven accurate in modeling density-driven flow under stable conditions, the accuracy of the MsFV method deteriorates in case of unstable flow and an iterative scheme is required to control the localization error. To avoid large computational overhead due to the iterative scheme, we suggest several adaptive strategies both for flow and transport. In particular, the concentration gradient is used to identify a front region where instabilities are triggered and an accurate (iteratively improved) solution is required. Outside the front region the problem is upscaled and both flow and transport are solved only at the coarse scale. This adaptive strategy leads to very accurate solutions at roughly the same computational cost as the non-iterative MsFV method. In many circumstances, however, an accurate description of flow instabilities requires a refinement of the computational grid rather than a coarsening. For these problems, we propose a modified iterative MsFV, which can be used as downscaling method (DMsFV). Compared to other grid refinement techniques the DMsFV clearly separates the computational domain into refined and non-refined regions, which can be treated separately and matched later. This gives great flexibility to employ different physical descriptions in different regions, where different equations could be solved, offering an excellent framework to construct hybrid methods.