  Using a recently developed piecewise flat method, numerical evolutions of the
Ricci flow are computed for a number of manifolds, using a number of different
mesh types, and shown to converge to the expected smooth behaviour as the mesh
resolution is increased. The manifolds were chosen to have varying degrees of
homogeneity, and include Nil and Gowdy manifolds, a three-torus initially
embedded in Euclidean four-space, and a perturbation of a flat three-torus. The
piecewise flat Ricci flow of the first two are shown to converge to known
smooth Ricci flow solutions, with the remaining two flowing asymptotically to
flat metrics.
