In this work we study different Implicit-Explicit (IMEX) schemes for incompressible flow problems with variable viscosity. Unlike most previous work on IMEX schemes, which focuses on the convective part, we here focus on treating parts of the diffusive term explicitly to reduce the coupling between the velocity components. We present different, both monolithic and fractional-step, IMEX alternatives for the variable-viscosity Navier--Stokes system, analysing their theoretical and algorithmic properties. Stability results are proven for all the methods presented, with all these results being unconditional, except for one of the discretisations using a fractional-step scheme, where a CFL condition (in terms of the problem data) is required for showing stability. Our analysis is supported by a series of numerical experiments.

翻译：本文研究适用于可变粘度不可压缩流问题的不同隐式-显式(IMEX)格式。与以往多数聚焦于对流项的IMEX格式研究不同，本文着重对扩散项中的部分分量进行显式处理，以降低速度分量之间的耦合。针对可变粘度纳维-斯托克斯系统，我们提出了包括整体式和分步式在内的多种IMEX替代方案，并分析了其理论与算法特性。本文对所有所述方法证明了稳定性结果，除采用分步格式的某一离散方案需满足（基于问题数据的）CFL条件外，其余所有结果均为无条件稳定。我们的分析得到了一系列数值实验的支持。