  It is well-known that the standard level set advection equation does not
preserve the signed distance property, which is a desirable property for the
level set function representing a moving interface. Therefore, reinitialization
or redistancing methods are frequently applied to restore the signed distance
property while keeping the zero-contour fixed. As an alternative approach to
these methods, we introduce a modified level set advection equation that
intrinsically preserves the norm of the gradient at the interface, i.e. the
local signed distance property. Mathematically, this is achieved by introducing
a carefully chosen source term being proportional to the local rate of
interfacial area generation. The introduction of the source term turns the
problem into a non-linear one. However, we show that by discretizing the source
term explicitly in time, it is sufficient to solve a linear equation in each
time step. Notably, without further adjustment, the method works in the case of
a moving contact line. This is a major advantage since redistancing is known to
be an issue when contact lines are involved. We provide a first implementation
of the method in a simple first-order upwind scheme in both two and three
spatial dimensions.
