  A brief review of the Stefan problem of solidification from a mixture, and
its main numerical solution methods is given. Simulation of this problem in 2D
or 3D is most practically done on a regular grid, where a sharp solid-liquid
interface moves relative to the grid. For this problem, a new simulation method
is developed that manifestly conserves mass, and that simulates the motion of
the interface to second order in the grid size. When applied to an isothermal
simulation of solidification from solution in 1D at 50% supersaturation for
only 5 grid points, the motion of the interface is accurate to 5.5%; and for 10
points the result is accurate to 1.5%. The method should be applicable to 2D or
3D with relative ease. This opens the door to large scale simulations with
modest computer power.
