论文标题
一种用于粘度可变流量的不可压缩流的光谱递延校正方法
A spectral deferred correction method for incompressible flow with variable viscosity
论文作者
论文摘要
本文介绍了一种半图形的光谱递延校正（SDC）方法，用于不可压缩的Navier-Stoke，它具有可变的粘度和时间依赖性边界条件的问题。所提出的方法整合了速度和压力校正方案的要素，该速度和压力校正方案比Minion＆Saye的SDPC方法更简单地处理压力处理和较小的分裂误差（J.Comput。375：797-822，2018）。结合了不连续的Galerkin光谱元素方法，用于空间离散化，从理论上讲，它可以达到时间和空间的任意准确性顺序。三个空间维度的数值实验在时间上表现为12阶，而在空间中有17个空间的实验，以实现恒定和变化，依赖溶液依赖性粘度。与SDPC相比，目前的方法可实质性地提高了由时间依赖性边界条件引起的降低降低的稳健性。
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.
