Three-dimensional (3D) simulation of facet formation and its coupled heat flow and segregation in the Bridgman growth of oxide crystals is presented. The growth of YAG crystals in the [1 1 1] direction, with {2 1 1} facets, is taken as an example to illustrate the finite volume treatment of the interfacial kinetics involving supercooling and crystallographic constrains. The simulation successfully reveals experimental observations, and the growth conditions for reducing faceting are consistent with growth experience in general. Increasing thermal gradients or reducing interface convexity reduces the faceting area. In addition, 3D convection and dopant segregation due to faceting are illustrated. The simulation also allows a different segregation coefficient at the facets, so that the abnormal segregation, such as the dark core, due to faceting can be simulated as well.