  This paper presents a semi-implicit spectral deferred correction (SDC) method
for incompressible Navier-Stokes problems with variable viscosity and
time-dependent boundary conditions. The proposed method integrates elements of
velocity- and pressure-correction schemes, which yields a simpler pressure
handling and a smaller splitting error than the SDPC method of Minion & Saye
(J. Comput. Phys. 375: 797-822, 2018). Combined with the discontinuous Galerkin
spectral-element method for spatial discretization it can in theory reach
arbitrary order of accuracy in time and space. Numerical experiments in three
space dimensions demonstrate up to order 12 in time and 17 in space for
constant as well as varying, solution-dependent viscosity. Compared to SDPC the
present method yields a substantial improvement of accuracy and robustness
against order reduction caused by time-dependent boundary conditions.
