  This paper investigates the competitiveness of semi-implicit Runge-Kutta (RK)
and spectral deferred correction (SDC) time-integration methods up to order six
for incompressible Navier-Stokes problems in conjunction with a high-order
discontinuous Galerkin method for space discretization. It is proposed to
harness the implicit and explicit RK parts as a partitioned scheme, which
provides a natural basis for the underlying projection scheme and yields a
straight-forward approach for accommodating nonlinear viscosity. Numerical
experiments on laminar flow, variable viscosity and transition to turbulence
are carried out to assess accuracy, convergence and computational efficiency.
Although the methods of order 3 or higher are susceptible to order reduction
due to time-dependent boundary conditions, two third-order RK methods are
identified that perform well in all test cases and clearly surpass all
second-order schemes including the popular extrapolated backward difference
method. The considered SDC methods are more accurate than the RK methods, but
become competitive only for relative errors smaller than ca $10^{-5}$.
