In this work, we present a novel isogeometric analysis discretization for the Navier-Stokes-Cahn-Hilliard equation, which uses divergence-conforming spaces. Basis functions generated with this method can have higher-order continuity, and allow to directly discretize the higherorder operators present in the equation. The discretization is implemented in PetIGA-MF, a high-performance framework for discrete differential forms. We present solutions in a twodimensional annulus, and model spinodal decomposition under shear flow.
Vignal, P., Sarmiento, A., Côrtes, A. M. A., Dalcin, L., & Calo, V. M. (2015). Coupling Navier-Stokes and Cahn-Hilliard equations in a two-dimensional annular flow configuration. In Procedia Computer Science (Vol. 51, pp. 934–943). Elsevier B.V. https://doi.org/10.1016/j.procs.2015.05.228