A spectral deferred correction method for incompressible flow with variable viscosity

01/31/2020

∙

by   Jörg Stiller, et al.

∙

0

∙

share

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 in comparison to 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, spatiotemporally varying as well as solution-dependent viscosity. The phenomenon of order reduction also reported by Minion Saye is observed in the case of time-dependent boundary conditions, where it manifests in terms of a slower convergence of the correction sweeps.