Multigrid by agglomeration for the acceleration of compressible flow calculations on unstructured meshes : Parallel computing issues and industrial applications

Carré, Gilles; Fournier, L.; Lanteri, Stéphane

doi:10.1007/bfb0106554

Cited by 5 publications

(10 citation statements)

References 5 publications

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“…Although conceptually different, PA-AMG is closely related to volume-agglomeration multigrid methods (see, e.g. [37][38][39]), which were preferably developed for the finite volume discretizations of hyperbolic problems. …”

Section: Algebraic Multigridmentioning

confidence: 99%

Truly monolithic algebraic multigrid for fluid–structure interaction

Gee

Küttler

Wall

2010

Numerical Meth Engineering

187

264

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SUMMARYThe coupling of flexible structures to incompressible fluids draws a lot of attention during the last decade. Many different solution schemes have been proposed. In this contribution, we concentrate on the strong coupling fluid-structure interaction by means of monolithic solution schemes. Therein, a Newton-Krylov method is applied to the monolithic set of nonlinear equations. Such schemes require good preconditioning to be efficient. We propose two preconditioners that apply algebraic multigrid techniques to the entire fluid-structure interaction system of equations. The first is based on a standard block Gauss-Seidel approach, where approximate inverses of the individual field blocks are based on a algebraic multigrid hierarchy tailored for the type of the underlying physical problem. The second is based on a monolithic coarsening scheme for the coupled system that makes use of prolongation and restriction projections constructed for the individual fields. The resulting nonsymmetric monolithic algebraic multigrid method therefore involves coupling of the fields on coarse approximations to the problem yielding significantly enhanced performance.

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Section: Algebraic Multigridmentioning

confidence: 99%

Truly monolithic algebraic multigrid for fluid–structure interaction

Gee

Küttler

Wall

2010

Numerical Meth Engineering

187

264

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“…This is the version used in matrix system (18). We want to compare the scale separation and the smallscale subgrid viscosity of various approaches regarding their dissipative effect along the scale spectrum.…”

Section: Remarkmentioning

confidence: 99%

“…The proposed Algebraic Variational Multiscale-Multigrid Method (AVM 3 ) as given by (18) with β = 0 is compared to three other methods:…”

Section: Remarkmentioning

confidence: 99%

“…It is noted that level-transfer techniques were also addressed in [15]. Furthermore, though conceptually different, PA-AMG is closely related to volume-agglomeration multigrid methods (see, e.g., [16][17][18]), which were preferably developed for finite-volume discretizations of hyperbolic problems. A similar scale separation, inspired by a volume-agglomeration method proposed in [16], had been used before in [19].…”

Section: Introductionmentioning

confidence: 98%

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An algebraic variational multiscale-multigrid method for large-eddy simulation: generalized-α time integration, Fourier analysis and application to turbulent flow past a square-section cylinder

et al. 2010

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This article studies three aspects of the recently proposed algebraic variational multiscale-multigrid method for large-eddy simulation of turbulent flow. First, the method is integrated into a second-order-accurate generalized-α time-stepping scheme. Second, a Fourier analysis of a simplified model problem is performed to assess the impact of scale separation on the overall performance of the method. The analysis reveals that scale separation implemented by projective operators provides modeling effects very close to an ideal small-scale subgrid viscosity, that is, it preserves low frequencies, in contrast to non-projective scale separations. Third, the algebraic variational multiscale-multigrid method is applied to turbulent flow past a square-section cylinder. The computational results obtained with the method reveal, on the one hand, the good accuracy achievable for this challenging test case already at a rather coarse discretization and, on the other hand, the superior computing efficiency, e.g., compared to a traditional dynamic Smagorinsky modeling approach.

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“…Part of its popularity derives from its capability to be implemented along with unstructured grids, employed for the representation of complicated geometries. Nevertheless, comparing to the structured solvers for the same test case, the unstructured ones seem to be relatively inefficient [2][3][4]. Moreover, using a finer spatial and angular discretization, higher-order accurate schemes [5,6] or a higher-order RTE [7] reduces even more the computational performance of such codes.…”

Section: Introductionmentioning

confidence: 99%

A parallel finite-volume spatial/angular agglomeration multigrid method for radiative heat transfer computation

Lygidakis¹,

Nikolos²

2014

WIT Transactions on Engineering Sciences

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The development of a spatial/angular agglomeration multigrid methodology is reported for the acceleration of a parallel node-centered finite-volume algorithm, numerically predicting radiative heat transfer in tetrahedral or hybrid unstructured grids. For spatial agglomeration, a sequence of coarser meshes is constructed, by merging the adjacent control volumes on a topology-preserving framework. Similarly, for the angular agglomeration, coarser angular resolutions are generated with the fusion of the neighbouring solid control angles, deriving a new angular discretization with the quarter number of control angles. The multigrid accelerated numerical solution of the Radiative Transfer Equation (RTE) is achieved via the Full Approximation Scheme (FAS) in a V-Cycle process. The proposed algorithm has been validated against benchmark test cases, demonstrating its capability for improved computational performance, especially in problems with purely scattering media and/or reflecting surfaces.

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Multigrid by agglomeration for the acceleration of compressible flow calculations on unstructured meshes : Parallel computing issues and industrial applications

Cited by 5 publications

References 5 publications

Truly monolithic algebraic multigrid for fluid–structure interaction

Truly monolithic algebraic multigrid for fluid–structure interaction

An algebraic variational multiscale-multigrid method for large-eddy simulation: generalized-α time integration, Fourier analysis and application to turbulent flow past a square-section cylinder

A parallel finite-volume spatial/angular agglomeration multigrid method for radiative heat transfer computation

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