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

A spectral deferred correction method for incompressible flow with variable viscosity