Overset meshes for incompressible flows: On preserving accuracy of underlying discretizations

Sharma, Ashesh; Ananthan, Shreyas; Sitaraman, Jayanarayanan; Thomas, Stephen J.; Sprague, Michael

doi:10.1016/j.jcp.2020.109987

Cited by 24 publications

(24 citation statements)

References 60 publications

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“…The open literature on overset grids has some studies on the topics listed above. But these employ either simple analytical solutions 18,19 which are far from the desired practical applications, or use industrial cases where the emphasis is validation. 8,[18][19][20] Due to the inherent complexity, numerical and modeling errors are then entangled and therefore difficult to quantify.…”

Section: Introductionmentioning

confidence: 99%

“…But these employ either simple analytical solutions 18,19 which are far from the desired practical applications, or use industrial cases where the emphasis is validation. 8,[18][19][20] Due to the inherent complexity, numerical and modeling errors are then entangled and therefore difficult to quantify. Moreover, in these papers, a small number of interpolation techniques are studied and rarely are accuracy, convergence order, robustness, and computational performance simultaneously and comprehensively analyzed.…”

Section: Introductionmentioning

confidence: 99%

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On the accuracy, robustness, and performance of high order interpolation schemes for the overset method on unstructured grids

Lemaire

Vaz

Rijswijk

et al. 2021

Numerical Methods in Fluids

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A comprehensive study on interpolation schemes used in overset grid techniques is here presented. Based on a literature review, numerous schemes are implemented, and their robustness, accuracy, and performance are assessed. Two code verification exercises are performed for this purpose: a 2D analytical solution of a laminar Poiseuille steady flow; and an intricate manufactured solution of a turbulent flow case, characteristic of a boundary layer flow combined with an unsteady separation bubble. For both cases, the influence of grid layouts, grid refinement, and time-step is investigated. Local and global errors, convergence orders, and mass imbalance are quantified. In terms of computational performance, strong scalability, cpu timings, load imbalancing, and domain connectivity information (DCI) overhead are reported. The effect of the overset-grid interpolation schemes on the numerical performance of the solver, that is, number of nonlinear iterations, is also scrutinized. The results show that, for a second order finite volume code, once diffusion is dominant (low Reynolds number), interpolation schemes higher than second order, for example, least squares of degree 2, are needed not to increase the total discretization errors. For convection dominated flows (high Reynolds numbers), the results suggest that second order schemes, for example, nearest cell gradient, are sufficient to prevent overset grid schemes to taint the underlying discretization errors. In terms of performance, by single-process and parallel communication optimization, the total overset-grid overhead (with DCI done externally to the CFD code) may be less than 4% of the total run time for second-order schemes and 8% for third-order ones, therefore empowering higher-order schemes and more accurate solutions.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the accuracy, robustness, and performance of high order interpolation schemes for the overset method on unstructured grids

Lemaire

Vaz

Rijswijk

et al. 2021

Numerical Methods in Fluids

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“…Nalu-Wind Model. Nalu-Wind solves the incompressible Navier-Stokes equations, with a pressure projection scheme [6]. The governing equations are discretized in time with a BDF-2 integrator, where an outer Picard fixed-point iteration is employed to reduce the nonlinear system residual at each time step.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…These high aspect ratios present a significant challenge. Overset meshes were employed [6] to generate body-fitted meshes for the wing and the wind tunnel geometry. The simulations were performed for the wing at 12 degree angle of attack, 1 m chord length, denoted c, 3.3 aspect ratio, i.e., s = 3.3c, and square wing tip.…”

Section: Numerical Resultsmentioning

confidence: 99%

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Neumann Series in GMRES and Algebraic Multigrid Smoothers

Thomas¹,

Arielle²,

Mullowney³

et al. 2021

Preprint

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Neumann series underlie both Krylov methods and algebraic multigrid smoothers. A low-synchronization modified Gram-Schmidt (MGS)-GMRES algorithm is described that employs a Neumann series to accelerate the projection step. A corollary to the backward stability result of Paige et al. [1] demonstrates that the truncated Neumann series approximation is sufficient for convergence of GMRES under standard conditions. The lower triangular solver associated with the correction matrix Tm = ( I + Lm ) −1 may then be replaced by a matrix-vector product with Tm = I − Lm. Next, Neumann series are applied to accelerate the classical Rüge-Stuben algebraic multigrid (AMG) preconditioner using either a polynomial Gauss-Seidel or incomplete ILU smoother. Here, the sparse triangular solver employed in the Gauss-Seidel and ILU smoothers is replaced by an inner iteration based upon matrix-vector products. Henrici's departure from normality of the associated iteration matrices leads to a better understanding of these series. Additionally, connections are made between the (non)normality of the L and U factors and nonlinear stability analysis, as well as the pseudospectra of the coefficient matrix. Furthermore, re-orderings that preserve structural symmetry also reduce the departure from normality of the upper triangular factor and improve the relative residual of the triangular solves. To demonstrate the effectiveness of this approach on many-core architectures, the proposed solver and preconditioner are applied to the pressure continuity equation for the incompressible Navier-Stokes equations of fluid motion. The pressure solve time is reduced considerably without a change in the convergence rate and the polynomial Gauss-Seidel smoother is compared with a Jacobi smoother. Numerical and timing results are presented for Nalu-Wind and the PeleLM combustion codes, where ILU with iterative triangular solvers is shown to be much more effective than polynomial Gauss-Seidel.

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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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Overset meshes for incompressible flows: On preserving accuracy of underlying discretizations

Cited by 24 publications

References 60 publications

On the accuracy, robustness, and performance of high order interpolation schemes for the overset method on unstructured grids

On the accuracy, robustness, and performance of high order interpolation schemes for the overset method on unstructured grids

Neumann Series in GMRES and Algebraic Multigrid Smoothers

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

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