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Nonconforming Schwarz-spectral element methods for incompressible flow. (English) Zbl 07124550
Summary: 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 boundary-data exchanges at each timestep or sub-timestep. Central to this implementation is a general, robust, and scalable interpolation routine, that rapidly determines the computational coordinates for arbitrary points \(\mathbf{x}^\ast = (x^\ast, y^\ast, z^\ast) \in \operatorname{\Omega} \subset \mathbb{R}^3\). The communication kernels in gslib execute with at most \(\log P\) complexity for \(P\) MPI ranks and have scaled to \(P > 10^6\). Given their performance and robustness, they obviate the need for development of additional MPI-based code for the Schwarz implementation and thus greatly simplify the development of a scalable parallel Schwarz solver. The communication overhead due to the boundary-data interpolation and exchange is only about 1% of the total time-to-solution for most cases. The original interpolation routine has been extended to support integer and real discriminator fields to choose which domain is responsible for interpolation when more than two subdomains overlap in a given region. We discuss the computation/communication complexity and accuracy of the approach, and present performance measurements for \(P > 12,000\) processors. We also demonstrate convergence results for the Schwarz-SEM formulation in multiple 2D and 3D configurations and present application of this method to several challenging fluid and heat transfer problems.

MSC:
76-XX Fluid mechanics
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