The MAC method

In this article recent advances in the Marker and Cell (MAC) method will be reviewed. The MAC technique dates back to the early 1960s at the Los Alamos Laboratories and this article starts with a historical review, and then a brief discussion of related techniques. Improvements since the early days of MAC (and the Simplified MAC – SMAC) include automatic time-stepping, the use of the conjugate gradient method to solve the Poisson equation for the corrected velocity potential, greater efficiency through stripping out the virtual particles (markers) other than those near the free surface, and more accurate approximations of the free surface boundary conditions, the addition of bounded high accuracy upwinding for the convected terms (thereby being able to solve higher Reynolds number flows), and a (dynamics) flow visualization facility. More recently, effective techniques for surface and interfacial flows and, in particular, for accurately tracking the associated surface(s)/interface(s) including moving contact angles have been developed. This article will concentrate principally on a three-dimensional version of the SMAC method. It will eschew both code verification and model validation; instead it will emphasize the applications that the MAC method can solve, from multiphase flows to rheology.