From Daniel Lörstad and Laszlo Fuchs, Journal of Computational Physics Volume 200, Issue 1, 10 October 2004, Pages 153-176
"The presence of discontinuous fields may compromise the convergence significantly. Hence, a few issues regarding multi-phase flows have to be addressed in order to maintain the convergence rate for large density ratio cases. The density field is computed at cell edges on the finest grid level using the phase distribution (described in the following section) and is transferred to the coarser grids. The density of one edge of a coarse cell of grid (m−1) is the average of the corresponding four cell edges on the finer grid (m). The viscosity field is obtained at cell centers and the value of a coarse cell on grid (m−1) is the average of the corresponding eight cells belonging to the finer grid (m). In order to maintain global mass conservation in each iteration, the sum of residuals of the continuity equation on coarser grids is always corrected to yield zero (i.e., global continuity). In addition, one has to ensure that the mass fluxes through the boundaries of the locally refined grids are conserved. Without global mass conservation, the MG solver cannot converge to machine accuracy (only to a level of the order of the truncation error)."