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 novel 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 source term that is 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 adjustment, the method works naturally 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 (see, e.g., Della Rocca and
Blanquart, 2014). We provide a first implementation of the method in a simple
first-order upwind scheme.Comment: 18 pages, 5 figure