Isogeometric divergence-conforming B-splines for the unsteady Navier–Stokes equations

Divergence-conforming B-splines are developed for application to the incompressible Navier–Stokes equations on geometrically mapped domains. These enable smooth, pointwise divergence-free solutions and thus satisfy mass conservation in the strongest possible sense. Semi-discrete methods based on divergence-conforming B-splines are shown to conserve linear and angular momentum and satisfy balance laws for energy, vorticity, enstrophy, and helicity. These are geometric structure-preserving quantities and numerical simulations that are sensitive to them are shown to be qualitatively correct and quantitatively accurate. The methods developed are anticipated to open new doors to the practical calculation of complex flows and to studies of their physical behavior.