In topography simulations the velocity field has no physical meaning, since the surface velocity can only be determined at points on the surface, where the surface velocity corresponds to the local deposition or etch rate. The LS method, however, requires a velocity field, for which the values must be known for at least all grid points which are updated in time. Hence, to enable the solution of the LS equation a technique is required which extrapolates the surface velocities from the surface to all those grid points.
Assuming that is available for all points , different techniques have been developed to obtain a surface velocity field which allows a stable time integration of the LS equation. In , it was proposed to define the surface velocity field as
A less costly technique to extrapolate the surface velocities based on an alternative formulation of the problem  is