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 and 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.

本文针对具有可变黏度和时变边界条件的不可压缩的Navier-Stokes问题，提出了一种半隐式谱延迟校正（SDC）方法。与Minion和Saye的SDPC方法相比，拟议的方法整合了速度和压力校正方案的要素，从而产生了更简单的压力处理和更小的分裂误差（J. Comput。Phys。375：797–822，2018）。结合不连续的Galerkin光谱元素方法进行空间离散化，理论上可以在时间和空间上达到任意精度的精度。在三个空间维度上的数值实验表明，对于恒定以及随溶液而变的粘度，时间上最高为12，空间上最高为17。