Divergence-conforming isogeometric collocation methods for the incompressible Navier–Stokes equations

We develop two isogeometric divergence-conforming collocation schemes for incompressible flow. The first is based on the standard, velocity–pressure formulation of Navier–Stokes equations, while second rotational form and includes vorticity as an unknown in addition to velocity pressure. describe process discretizing each using B-splines that conform a discrete de Rham complex collocating governing equation at Greville abcissae corresponding space. Results mapped domains are obtained by mapping equations back parametric domain structure-preserving transformations. Numerical results show promise method, including accelerated convergence rates three field, vorticity–velocity–pressure scheme when compared scheme.