Abstract

In this talk, I will present a novel structure-preserving numerical method for gradient flows with respect to Wasserstein-like transport distances induced by concentration-dependent mobilities, which arise widely in materials science and biology. Based upon the minimizing movement scheme and the dynamical characterization of the transport distances, we construct a fully discrete scheme that ends up with a minimization problem with strictly convex objective functions and a linear constraint. By utilizing the underlying variational structure and modern operator-splitting schemes, our method has built-in positivity or boundedness preserving, mass conservation, and energy-dissipative structures. I will show the flexibility and performance of our methods through a suite of simulation examples including different free energy functionals, wetting boundary conditions and degenerate mobilities.