论文标题
在重叠网格中的不可压缩的Navier-Stokes方程的多次时间播放
Multirate Timestepping for the Incompressible Navier-Stokes Equations in Overlapping Grids
论文作者
论文摘要
我们开发了一个多级时间，用于基于最近开发的多域光谱元素方法（SEM）的不稳定不可压缩的Navier-Stokes方程（INSE）的半图像解决方案。对于{\ em不可压缩}流，由于不可压缩性约束所隐含的紧密耦合，多次时间播放（MTS）特别具有挑战性，这表现为每个时间步中压力的椭圆s子问题。我们方法的新颖性源于直接应用于Navier-Stokes方程的稳定重叠的Schwarz方法的发展，而不是大多数INSE求解器核心的对流，粘性和压力取代。我们的MTS方法是基于预测校正器（PC）策略，该策略保留了基础半平移时间的时间融合。我们提出了数值结果，表明该方法缩放到任意数量的重叠网格，准确地对复杂的湍流现象进行建模，并提高了与基于Singlerate时间播放的计算相比的计算效率。
We develop a multirate timestepper for semi-implicit solutions of the unsteady incompressible Navier-Stokes equations (INSE) based on a recently-developed multidomain spectral element method (SEM). For {\em incompressible} flows, multirate timestepping (MTS) is particularly challenging because of the tight coupling implied by the incompressibility constraint, which manifests as an elliptic subproblem for the pressure at each timestep. The novelty of our approach stems from the development of a stable overlapping Schwarz method applied directly to the Navier-Stokes equations, rather than to the convective, viscous, and pressure substeps that are at the heart of most INSE solvers. Our MTS approach is based on a predictor-corrector (PC) strategy that preserves the temporal convergence of the underlying semi-implicit timestepper. We present numerical results demonstrating that this approach scales to an arbitrary number of overlapping grids, accurately models complex turbulent flow phenomenon, and improves computational efficiency in comparison to singlerate timestepping-based calculations.
