  This paper is devoted to the robust approximation with a variational phase
field approach of multiphase mean curvature flows with possibly highly
contrasted mobilities. The case of harmonically additive mobilities has been
addressed recently using a suitable metric to define the gradient flow of the
phase field approximate energy. We generalize this approach to arbitrary
nonnegative mobilities using a decomposition as sums of harmonically additive
mobilities. We establish the consistency of the resulting method by analyzing
the sharp interface limit of the flow: a formal expansion of the phase field
shows that the method is of second order. We propose a simple numerical scheme
to approximate the solutions to our new model. Finally, we present some
numerical experiments in dimensions 2 and 3 that illustrate the interest and
effectiveness of our approach, in particular for approximating flows in which
the mobility of some phases is zero.
