An implicit multigrid method by agglomeration applied to turbulent flows

Carré, Gilles

doi:10.1016/s0045-7930(96)00045-x

Cited by 18 publications

(10 citation statements)

References 18 publications

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“…For technical reasons, the final agglomerated grid could not be effectively shown. A result of a first-order computation for a fairly fine mesh over the wing is shown in Figure 5, and is compared with experimental results [17,18] (Figure 1(b)). The initial grid includes 313 424 cells and 66 467 nodes.…”

Section: Verificationmentioning

confidence: 99%

Multigrid convergence acceleration for implicit and explicit solution of Euler equations on unstructured grids

Ramezani

Mazaheri

2009

Numerical Methods in Fluids

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SUMMARYThe multigrid method is one of the most efficient techniques for convergence acceleration of iterative methods. In this method, a grid coarsening algorithm is required. Here, an agglomeration scheme is introduced, which is applicable in both cell-center and cell-vertex 2 and 3D discretizations. A new implicit formulation is presented, which results in better computation efficiency, when added to the multigrid scheme. A few simple procedures are also proposed and applied to provide even higher convergence acceleration. The Euler equations are solved on an unstructured grid around standard transonic configurations to validate the algorithm and to assess its superiority to conventional explicit agglomeration schemes. The scheme is applied to 2 and 3D test cases using both cell-center and cell-vertex discretizations.

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Section: Verificationmentioning

confidence: 99%

Multigrid convergence acceleration for implicit and explicit solution of Euler equations on unstructured grids

Ramezani

Mazaheri

2009

Numerical Methods in Fluids

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“…3. Linear multigrid (LMG): In this approach [44,45] MG is applied to the iterative technique used to solve the linear system resulting from the implicit time discretization of the equations [56] (this was also termed Newton MG iteration by Hackbusch [56]), and as such can be applied to turbulence transport without any particular stabilization fix. Linear multigrid (LMG) can be efficient provided the solution of the linear system corresponds to a large percentage of CPU usage for the SG algorithm [76].…”

Section: Introductionmentioning

confidence: 99%

Implicit meanflow–multigrid algorithms for Reynolds stress model computation of 3‐D anisotropy‐driven and compressible flows

Gerolymos

Vallet

2008

Numerical Methods in Fluids

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SUMMARYThe present paper investigates the multigrid (MG) acceleration of compressible Reynolds-averaged Navier-Stokes computations using Reynolds-stress model 7-equation turbulence closures, as well as lowerlevel 2-equation models. The basic single-grid SG algorithm combines upwind-biased discretization with a subiterative local-dual-time-stepping time-integration procedure. MG acceleration, using characteristic MG restriction and prolongation operators, is applied on meanflow variables only (MF-MG), turbulence variables being simply injected onto coarser grids. A previously developed non-time-consistent (for steady flows) full-approximation-multigrid (s-MG) is assessed for 3-D anisotropy-driven and/or separated flows, which are dominated by the convergence of turbulence variables. Even for these difficult test cases CPU-speed-ups r CPUSUP ∈[3, 5] are obtained. Alternative, potentially time-consistent approaches (unsteady u-MG), where MG acceleration is applied at each subiteration, are also examined, using different subiterative strategies, MG cycles, and turbulence models. For 2-D shock wave/turbulent boundary layer interaction, the fastest s-MG approach, with a V(2, 0) sawtooth cycle, systematically yields CPU-speed-ups of 5± 1 2 , quasi-independent of the particular turbulence closure used.

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“…As with many iterative solvers, multigrid methods can be used directly as nonlinear solvers [1][2][3] or as linear solvers operating on a linearization arising from a Newton solution strategy for the nonlinear problem at hand [4][5][6]. In addition, multigrid methods can also be used as a linear or nonlinear preconditioner for a Newton-Krylov method [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

An Assessment of Linear Versus Nonlinear Multigrid Methods for Unstructured Mesh Solvers

Mavriplis

2002

Journal of Computational Physics

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The relative performance of a nonlinear full approximation storage multigrid algorithm and an equivalent linear multigrid algorithm for solving two different nonlinear problems is investigated. The first case consists of a transient radiation diffusion problem for which an exact linearization is available, while the second problem involves the solution of the steady-state Navier-Stokes equations, where a first-order discrete Jacobian is employed as an approximation to the Jacobian of a secondorder-accurate discretization. When an exact linearization is employed, the linear and nonlinear multigrid methods asymptotically converge at identical rates and the linear method is found to be more efficient due to its lower cost per cycle. When an approximate linearization is employed, as in the Navier-Stokes cases, the relative efficiency of the linear approach versus the nonlinear approach depends both on the degree to which the linear system approximates the full Jacobian as well as on the relative cost of linear versus nonlinear multigrid cycles. For cases where convergence is limited by a poor Jacobian approximation, substantial speedup can be obtained using either multigrid method as a preconditioner to a Newton-Krylov method. c 2002 Elsevier Science

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An implicit multigrid method by agglomeration applied to turbulent flows

Cited by 18 publications

References 18 publications

Multigrid convergence acceleration for implicit and explicit solution of Euler equations on unstructured grids

Multigrid convergence acceleration for implicit and explicit solution of Euler equations on unstructured grids

Implicit meanflow–multigrid algorithms for Reynolds stress model computation of 3‐D anisotropy‐driven and compressible flows

An Assessment of Linear Versus Nonlinear Multigrid Methods for Unstructured Mesh Solvers

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