29 Search Results

The solution to the Poisson equation arising from the spectral element discretization of the incompressible Navier-Stokes equations requires robust preconditioning strategies. One such strategy is multigrid. To realize the potential of multigrid methods, effective smoothing strategies are needed. Chebyshev polynomial smoothers, in conjunction with pointwise Jacobi or additive Schwarz methods (ASMs), prove to be an effective smoother. Other polynomial smoothers, however, may provide superior convergence to the multigrid preconditioner. The authors compare the standard Chebyshev polynomial smoothers to both the novel fourth-kind Chebyshev polynomial smoothers proposed by Lottes as well as smoothers based on the polynomial of best uniform approximationmore » to as proposed by Kraus, Vassilevski, and Zikatanov. At the cost of symmetry, further improvements may be made. For example, a order polynomial smoother on both sides of the V-cycle may be substituted with an order polynomial smoother on one side at no additional cost. The choice of omitting the postsmoother in favor of higher-order polynomial presmoothing is advantageous in cases where the multigrid approximation property constant is large. The authors consider a 2D model problem based on finite differences to motivate the choice of polynomial smoother, order, and whether to apply postsmoothing for the target application of high-order -geometric multigrid methods for GPU architectures. Results from both domains demonstrate the substantial improvement of these approaches over the standard Chebyshev polynomial smoother with a symmetric V-cycle.« less

Robust and scalable function evaluation at any arbitrary point in the finite/spectral element mesh is required for querying the partial differential equation solution at points of interest, comparison of solution between different meshes, and Lagrangian particle tracking. This is a challenging problem, particularly for high-order unstructured meshes partitioned in parallel with MPI, as it requires identifying the element that overlaps a given point and computing the corresponding reference space coordinates. Here, we present a robust and efficient technique for general field evaluation in large-scale high-order meshes with quadrilaterals and hexahedra. In the proposed method, a combination of globally partitioned andmore » processor-local maps are used to first determine a list of candidate MPI ranks, and then locally candidate elements that could contain a given point. Next, element-wise bounding boxes further reduce the list of candidate elements. Finally, Newton’s method with trust region is used to determine the overlapping element and corresponding reference space coordinates. Since GPU-based architectures have become popular for accelerating computational analyses using meshes with tensor-product elements, specialized kernels have been developed to utilize the proposed methodology on GPUs. The method is also extended to enable general field evaluation on surface meshes. The paper concludes by demonstrating the use of the proposed method in various applications ranging from mesh-to-mesh transfer during r-adaptivity to Lagrangian particle tracking.« less

The authors explore performance scalability of the open-source thermal-fluids code, NekRS, on the U.S. Department of Energy's leadership computers, Crusher, Frontier, Summit, Perlmutter, and Polaris. Particular attention is given to analyzing performance and time-to-solution at the strong-scale limit for a target efficiency of 80%, which is typical for production runs on the DOE's high-performance computing systems. Several examples of anomalous behavior are also discussed and analyzed.

Packed beds are commonly found in many engineering systems and have been widely studied for decades. A relatively new packed bed system is the Pebble Bed Reactor, a type of generation-IV nuclear reactor. Unlike many of the packed beds encountered in chemical and process engineering applications, Pebble Bed Reactors are larger and operate at significantly higher Reynolds numbers. As a result of these differences, there is a very limited amount of information on the detailed flow physics that exist in these complex geometries. This work seeks to contribute to a growing database of flow data for Pebble Bed Reactor systemsmore » by performing Direct Numerical Simulations of the flow in an experimental bed of 67 pebbles for a range of conditions. Simulations are performed at a Prandtl number of 0.66 and Reynolds numbers from 300–600. These Reynolds numbers are chosen to gain additional knowledge on the spatial development of turbulence in these systems. Analysis of the Turbulent Kinetic Energy, turbulence anisotropy, and Turbulent Heat Flux is performed. Results demonstrate significant development of the TKE across the tested range of Reynolds numbers. Examination of both the TKE and THF reveal that development first occurs near the center of the bed and propagates radially as the flow moves further into the bed. Notable regions of negative production of turbulent kinetic energy are observed in regions where flow accelerates around pebble contact points. Furthermore, these regions are found to coincide with regions of 1-component turbulence.Kindly check and confirm, all authors email id is correctly identified.These are correct« less

We examine large-eddy-simulation modeling approaches and computational performance of two open-source computational fluid dynamics codes for the simulation of atmospheric boundary layer flows that are of direct relevance to wind energy production. The first code, NekRS, is a high-order, unstructured-grid, spectral element code. The second code, AMR-Wind, is a second-order, block-structured, finite-volume code with adaptive mesh refinement capabilities. The objective of this study is to co-develop these codes in order to improve model fidelity and performance for each. These features will be critical for running ABL-based applications such as wind farm analysis on advanced computing architectures. To this end, wemore » investigate the performance of NekRS and AMR-Wind on the Oak Ridge Leadership Facility supercomputers Summit, using 4 to 800 nodes (24 to 4,800 NVIDIA V100 GPUs), and Crusher, the testbed for the Frontier exascale system, using 18 to 384 Graphics Compute Dies on AMD MI250X GPUs. We compare strong- and weak-scaling capabilities, linear solver performance, and time to solution. We also identify leading inhibitors to parallel scaling.« less

Development and application of the open-source GPU-based fluid-thermal simulation code, NekRS, are described. Time advancement is based on an efficient kth-order accurate timesplit formulation coupled with scalable iterative solvers. Spatial discretization is based on the high-order spectral element method (SEM), which affords the use of fast, low-memory, matrix-free operator evaluation. Further, recent developments include support for nonconforming meshes using overset grids and for GPU-based Lagrangian particle tracking. Results of large-eddy simulations of atmospheric boundary layers for wind-energy applications as well as extensive nuclear energy applications are presented.

The authors introduce an augmented-basis method (ABM) to stabilize reduced-order models (ROMs) of turbulent incompressible flows. The method begins with standard basis functions derived from proper orthogonal decomposition (POD) of snapshot sets taken from a full-order model. These are then augmented with divergence-free projections of a subset of the nonlinear interaction terms that constitute a significant fraction of the time-derivative of the solution. The augmenting bases, which are rich in localized high wavenumber content, are better able to dissipate turbulent kinetic energy than the standard POD bases. Several examples illustrate that the ABM significantly out-performs L ² -, H ¹more » - and Leray-stabilized POD ROM approaches. The ABM yields accuracy that is comparable to constraint-based stabilization approaches yet is suitable for parametric model-order reduction in which one uses the ROM to evaluate quantities of interests at parameter values that differ from those used to generate the full-order model snapshots. Several numerical experiments point to the importance of localized high wavenumber content in the generation of stable, accurate, and efficient ROMs for turbulent flows.« less

A time-averaged error indicator with POD- h Greedy is developed to drive parametric model order reduction (pMOR) for 2D unsteady natural convection in a high-aspect ratio slot parameterized with the Prandtl number, Rayleigh number, and slot angle with respect to the gravity. The error indicator is extended to accommodate the energy equation and Leray regularization. Despite being two-dimensional and laminar, the target flow regime presents several challenges: 1) there is a bifurcation in the angle parameter space; 2) the solution can be multivalued, even at steady state; and 3) the solution exhibits spatio-temporal chaos at several points in the parametermore » space. The authors explore several reduced-order models (ROMs) and demonstrate that Leray-regularized Galerkin ROMs provide a robust solution approach for this class of flows. They further demonstrate that error-indicated pMOR can efficiently predict several QOIs, such as mean flow, mean Nusselt number and mean turbulent kinetic energy, even in the presence of a bifurcation. Finally, they show that spatio-temporal chaos can lead to lack of reproducibility in both the full-order model and the reduced-order model and that the variance in the full-order model provides a lower bound on the pMOR error in these cases.« less

Packed beds play an important role in several engineering fields, with their applications in nuclear energy being driven by the development of next-generation reactors utilizing pebble fuel. The random nature of a packed pebble bed creates a flow field that is complex and difficult to predict. Porous media models are an attractive option for modeling pebble-bed reactors (PBRs), as they provide intermediate fidelity results and are computationally efficient. Porous media models, however, rely on the use of correlations to estimate the effect of complicated flow features on the pressure drop and heat transfer in the system. Existing correlations were developedmore » to predict the average behavior of the bed, but they are inaccurate in the near-wall region where the presence of the wall affects the pebble packing. This work aims to investigate the accuracy of a porous media model using the Kerntechnischer Ausschuss (KTA) correlation, the most common pressure drop correlation for PBRs compared to the high-fidelity large eddy simulation (LES). A bed of 1568 pebbles is investigated at Reynolds numbers from 625 to 10 000. The bed is divided into five concentric subdomains to compare the average velocity, friction losses, and form losses between the porous media and LES codes. The comparison between the LES simulation and the KTA correlation revealed that the KTA correlation largely underpredicts the form losses in the near-wall region, leading to an overprediction of the velocity near the wall by nearly 30%. An investigation of the form losses across the range of Reynolds numbers in the LES results provided additional insight into how the KTA correlation may be improved to better predict these spatial effects in a pebble bed. These data suggest that the form coefficient near the wall must be increased by 48% while decreasing the form coefficient of the inner bulk region of the bed by 15%. The implementation of these improvements to the KTA correlation in a porous media model produced a radial velocity profile that saw significantly improved agreement with the LES results.« less