Effects of using altered coarse grids on the implementation and computational cost of the multiscale finite volume method

• A multiscale finite volume method is implemented on an altered coarse grid.
• The computational cost and reconstruction step differ from the basic MsFV method.
• Two reconstruction procedures are proposed and compared.
• The matrix formulation is given and compared with that of the original MsFV method.

In the present work, the multiscale finite volume (MsFV) method is implemented on a new coarse grids arrangement. Like grids used in the MsFV methods, the new grid arrangement consists of both coarse and dual coarse grids but here each coarse block in the MsFV method is a dual coarse block and vice versa. Due to using the altered coarse grids, implementation, computational cost, and the reconstruction step differ from the original version of MsFV method. Two reconstruction procedures are proposed and their performances are compared with each other. For a wide range of 2-D and 3-D problem sizes and coarsening ratios, the computational costs of the MsFV methods are investigated. Furthermore, a matrix (operator) formulation is presented. Several 2-D test cases, including homogeneous and heterogeneous permeability fields extracted from different layers of the tenth SPE comparative study problem are solved. The results are compared with the fine-scale reference and basic MsFV solutions.