Multiphase mean curvature flows approximation : the case of non harmonically additive mobilities

This paper concerns the robust approximation of multi-phase mean curvature flow by phase fields even when the phase mobility are highly contrasted. Recent work suggested that harmonically additive mobilities could be incorporated in the metric of the associated gradient flow. We generalize this approach to arbitrary mobilities, by splitting them as a sum of a 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 order 2. Finally, we present some numerical experiments in dimensions $2$ and $3$ that illustrate the interest of our method, in particular in the modeling of flows in which some of the phases have 0 or infinite mobility.