A Comparison of Classical and Aggregation-Based Algebraic Multigrid Preconditioners for High-Fidelity Simulation of Wind Turbine Incompressible Flows

Thomas, Stephen J.; Ananthan, Shreyas; Yellapantula, Shashank; Hu, Jonathan J.; Lawson, Michael; Sprague, Mary Ann

doi:10.1137/18m1179018

Cited by 12 publications

(13 citation statements)

References 23 publications

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“…The linear system employed for GPU performance analysis was extracted from the Nalu Vestas V27 wind turbine simulation described in Thomas et al 1 The matrix has 675,905 rows and 675,905 columns. The average number of nonzeros per row is 11.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Krylov solvers are common in applications such as fluid flow simulations based on finite element discretizations of partial differential equations (PDEs). These solvers account for a substantial amount of the total run‐time (e.g., ≈30 % in Thomas et al 1 ). The focus of this paper is on improving the performance of the Generalized Minimal Residual Method (GMRES) 2 .…”

Section: Introductionmentioning

confidence: 99%

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Low synchronization Gram–Schmidt and generalized minimal residual algorithms

Swirydowicz

Langou

Ananthan

et al. 2020

Numerical Linear Algebra App

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Summary The Gram–Schmidt process uses orthogonal projection to construct the A = QR factorization of a matrix. When Q has linearly independent columns, the operator P = I − Q(QTQ)−1QT defines an orthogonal projection onto Q⊥. In finite precision, Q loses orthogonality as the factorization progresses. A family of approximate projections is derived with the form P = I − QTQT, with correction matrix T. When T = (QTQ)−1, and T is triangular, it is postulated that the best achievable orthogonality is 𝒪(ε)κ(A). We present new variants of modified (MGS) and classical Gram–Schmidt algorithms that require one global reduction step. An interesting form of the projector leads to a compact WY representation for MGS. In particular, the inverse compact WY MGS algorithm is equivalent to a lower triangular solve. Our main contribution is to introduce a backward normalization lag into the compact WY representation, resulting in a 𝒪(ε)κ([r0,AVm]) stable Generalized Minimal Residual Method (GMRES) algorithm that requires only one global reduce per iteration. Further improvements in performance are achieved by accelerating GMRES on GPUs.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Low synchronization Gram–Schmidt and generalized minimal residual algorithms

Swirydowicz

Langou

Ananthan

et al. 2020

Numerical Linear Algebra App

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“…An incremental approximate pressure‐projection algorithm 50,51 calculates momentum and pressure solutions at each time step. We solve a set number of Picard iterations,

K

, with the solution initialized to

{bold-italicu}_{0}^{n + 1} = {bold-italicu}_{K}^{n}

and

p_{0}^{n + 1} = p_{K}^{n}

at each time step.…”

Section: Cfd Solversmentioning

confidence: 99%

ExaWind: Open‐source CFD for hybrid‐RANS/LES geometry‐resolved wind turbine simulations in atmospheric flows

Sharma,

Brazell,

Vijayakumar

et al. 2024

Wind Energy

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Predictive high‐fidelity modeling of wind turbines with computational fluid dynamics, wherein turbine geometry is resolved in an atmospheric boundary layer, is important to understanding complex flow accounting for design strategies and operational phenomena such as blade erosion, pitch‐control, stall/vortex‐induced vibrations, and aftermarket add‐ons. The biggest challenge with high‐fidelity modeling is the realization of numerical algorithms that can capture the relevant physics in detail through effective use of high‐performance computing. For modern supercomputers, that means relying on GPUs for acceleration. In this paper, we present ExaWind, a GPU‐enabled open‐source incompressible‐flow hybrid‐computational fluid dynamics framework, comprising the near‐body unstructured grid solver Nalu‐Wind, and the off‐body block‐structured‐grid solver AMR‐Wind, which are coupled using the Topology Independent Overset Grid Assembler. Turbine simulations employ either a pure Reynolds‐averaged Navier–Stokes turbulence model or hybrid turbulence modeling wherein Reynolds‐averaged Navier–Stokes is used for near‐body flow and large eddy simulation is used for off‐body flow. Being two‐way coupled through overset grids, the two solvers enable simulation of flows across a huge range of length scales, for example, 10 orders of magnitude going from O(μm) boundary layers along the blades to O(10 km) across a wind farm. In this paper, we describe the numerical algorithms for geometry‐resolved turbine simulations in atmospheric boundary layers using ExaWind. We present verification studies using canonical flow problems. Validation studies are presented using megawatt‐scale turbines established in literature. Additionally presented are demonstration simulations of a small wind farm under atmospheric inflow with different stability states.

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“…The right-hand side contains the appropriate terms, e.g., for a non-solenoidal velocity field. For more details, see Thomas et al 3 In order to derive a projection scheme, consider the time-split system of equations,…”

Section: Exawind Wind-turbine Modelmentioning

confidence: 99%

“…We consider an incomplete LU (e.g., ILU(k), ILUTP) 1 factorization used within the Algebraic Multigrid (AMG) method for the low Mach Navier-Stokes pressure solvers, PeleLM 2 and Nalu-Wind. 3 Analogous geometric multigrid methods (GMG) are employed in the NekRS 4,5 and ExaDG 6 pressure solvers. GMG operates on a hierarchy of nested grids with different resolutions and is effective for structured grid problems where the underlying mesh has a well-defined geometric structure.…”

Section: Introductionmentioning

confidence: 99%

Scaled ILU smoothers for Navier–Stokes pressure projection

Thomas,

Carr,

Mullowney

et al. 2023

Numerical Methods in Fluids

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Incomplete LU (ILU) smoothers are effective in the algebraic multigrid (AMG) ‐cycle for reducing high‐frequency components of the error. However, the requisite direct triangular solves are comparatively slow on GPUs. Previous work has demonstrated the advantages of Jacobi iteration as an alternative to direct solution of these systems. Depending on the threshold and fill‐level parameters chosen, the factors can be highly nonnormal and Jacobi is unlikely to converge in a low number of iterations. We demonstrate that row scaling can reduce the departure from normality, allowing us to replace the inherently sequential solve with a rapidly converging Richardson iteration. There are several advantages beyond the lower compute time. Scaling is performed locally for a diagonal block of the global matrix because it is applied directly to the factor. Further, an ILUT Schur complement smoother maintains a constant GMRES iteration count as the number of MPI ranks increases, and thus parallel strong‐scaling is improved. Our algorithms have been incorporated into hypre, and we demonstrate improved time to solution for linear systems arising in the Nalu‐Wind and PeleLM pressure solvers. For large problem sizes, GMRESAMG executes at least five times faster when using iterative triangular solves compared with direct solves on massively parallel GPUs.

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A Comparison of Classical and Aggregation-Based Algebraic Multigrid Preconditioners for High-Fidelity Simulation of Wind Turbine Incompressible Flows

Cited by 12 publications

References 23 publications

Low synchronization Gram–Schmidt and generalized minimal residual algorithms

Low synchronization Gram–Schmidt and generalized minimal residual algorithms

ExaWind: Open‐source CFD for hybrid‐RANS/LES geometry‐resolved wind turbine simulations in atmospheric flows

Scaled ILU smoothers for Navier–Stokes pressure projection

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