Contributed Talk
IMEX Time Integration for Divergence-Conforming Isogeometric Collocation in Incompressible Navier–Stokes Problems
Scuola Superiore Meridionale, Napoli, Italy
Abstract
Isogeometric collocation is a computationally efficient alternative to Galerkin methods, achieving high-order accuracy with fewer degrees of freedom by enforcing the strong form of partial differential equations (PDEs). In incompressible flow problems, divergence-conforming collocation schemes ensure a pointwise divergence-free velocity field. We study the impact of time integration strategies based on implicit–explicit (IMEX) schemes for the Navier–Stokes equations, treating the nonlinear, convective terms explicitly and the diffusive terms implicitly. This separation not only enhances computational efficiency but also maintains the divergence-conforming structure of the discretization, preserving the exactness of the mass equation pointwise. We detail the implementation of the IMEX framework and support the methodology with a series of numerical experiments on high-Reynolds-number flows.