  We have developed a new embedding method for solving scalar hyperbolic
conservation laws on surfaces. The approach represents the interface implicitly
by a signed distance function following the typical level set method and some
embedding methods. Instead of solving the equation explicitly on the surface,
we introduce a modified partial differential equation in a small neighborhood
of the interface. This embedding equation is developed based on a push-forward
operator that can extend any tangential flux vectors from the surface to a
neighboring level surface. This operator is easy to compute and involves only
the level set function and the corresponding Hessian. The resulting solution is
constant in the normal direction of the interface. To demonstrate the accuracy
and effectiveness of our method, we provide some two- and three-dimensional
examples.
