不可压缩流的非协调Schwarz谱元方法
Nonconforming Schwarz-Spectral Element Methods For Incompressible Flow
摘要：
我们提出了基于谱元的Schwarz重叠（重叠）方法的不可压缩Navier-Stokes（NS）方程的可扩展实现。我们的基于SEM的重叠网格方法在NS方程的水平上实现，NS方程在每个时间步或子时间步使用域间速度和压力边界数据交换在单独的子域内独立地推进。该实现的核心是一个通用的、鲁棒的和可缩放的插值例程{ \em gslib-findpts}，它快速确定任意点$\mathbf{x}^* =(x^*,y^*,z^*) \in Ω\subset {\rm I\!R}^3$的计算坐标（处理器$p$、元素编号$e$和局部坐标$(r,s,t) \in \hatΩ := [-1,1]^3$）。$gslib$中的通信内核以最多$P$ MPI等级的$\log P$复杂度执行，已扩展到$P > 10^6$，并满足了为Schwarz实现开发任何其他基于MPI的代码的需求。原来的插值程序已被扩展到多个重叠的领域。新的实现区分拥有子域的距离域边界，这样的接口边界数据是从最内的内部点。我们目前的应用这种方法的几个传热和流体动力学问题，讨论的计算/通信的复杂性和准确性的方法，并提出性能测量$P > 12,000$。
英文摘要：
We present scalable implementations of spectral-element-based Schwarz overlapping (overset) methods for the incompressible Navier-Stokes (NS) equations. Our SEM-based overset grid method is implemented at the level of the NS equations, which are advanced independently within separate subdomains using interdomain velocity and pressure boundary-data exchanges at each timestep or sub-timestep. Central to this implementation is a general, robust, and scalable interpolation routine, {\em gslib-findpts}, that rapidly determines the computational coordinates (processor $p$, element number $e$, and local coordinates $(r,s,t) \in \hatΩ := [-1,1]^3$) for any arbitrary point $\mathbf{x}^* =(x^*,y^*,z^*) \in Ω\subset {\rm I\!R}^3$. The communication kernels in $gslib$ execute with at most $\log P$ complexity for $P$ MPI ranks, have scaled to $P > 10^6$, and obviate the need for development of any additional MPI-based code for the Schwarz implementation. The original interpolation routine has been extended to account for multiple overlapping domains. The new implementation discriminates the possessing subdomain by distance to the domain boundary, such that the interface boundary data is taken from the inner-most interior points. We present application of this approach to several heat transfer and fluid dynamic problems, discuss the computation/communication complexity and accuracy of the approach, and present performance measurements for $P > 12,000$.
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