The solidification processing of metal matrix composites is investigated using a modified enthalpy method that can account for the presence of the discontinuous reinforcing phase. The propagation of the solid liquid interface is tracked through the complicated, microscale domain formed by the fibers. Conduction in the matrix as well as in the dispersed phase is considered. The fixed-grid, single-domain computational approach presented is much more efficient than a previous three-domain approach reported in the literature. Results obtained from the simulations compare well with those in the literature in terms of the shape of the interface obtained and its movement in the presence of low- and high-conductivity fibers. Important extensions to the work are outlined, primary among these being the inclusion of the effects of melt convection and solutal gradients.