Multigrid algorithm for three-dimensional incompressible high-Reynolds number turbulent flows

Sheng, Chunhua; Taylor, Lafayette K.; Whitfield, David L.

doi:10.2514/3.12949

Cited by 21 publications

(18 citation statements)

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“…To be parallel with compressible flow solvers, upwind characteristic-based schemes are frequently used. In this work, Roe's flux-splitting scheme is used in conjunction with Van Leer's MUSCL formulation, which was first applied to incompressible flows by Whitfield and co-workers [11,31]. Taking the ξ direction as an example, the inviscid derivative is discretized as…”

Section: Time and Spatial Discretizationsmentioning

confidence: 99%

“…Numerous studies have reported successful implementation of the MG method in compressible [25] and incompressible flow problems [26][27][28], and its performance to accelerate convergence is very impressive. However, there are only a few studies [29][30][31][32] that developed MG methods in conjunction with the ACM, and all are exclusively based on the cell-centered finite volume discretization; see the brief review by Drikakis et al [32]. Applications to unsteady flow computations and implementations in conjunction with a collocated finite difference discretization are limited.…”

Section: Introductionmentioning

confidence: 99%

“…The author also tried the LU-SGS scheme [18,38] and the approximation factorization-planar symmetric Gauss-Seidel scheme [13] and found that the overall computing time was greater than that of the diagonalized ADI scheme; thus these implicit schemes were excluded in this work. The discretization for the convective terms used is an upwind differencing scheme based on Roe's approximate Riemann solver [39] with Van Leer's MUSCL formulation [40], which was applied to the ACM and recommended for its computational efficiency and accuracy in [11,31]. The MUSCL formulation was usually used together with limiters, but it was found that they are not necessary for the present cases.…”

Section: Introductionmentioning

confidence: 99%

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Comparison of Implicit Multigrid Schemes for Three-Dimensional Incompressible Flows

2002

Journal of Computational Physics

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To develop a robust and efficient computational flow simulation tool for incompressible flow applications, a number of different implicit multigrid schemes for solving the three-dimensional incompressible Navier-Stokes equations are compared in the current study. These schemes consist of a common full approximation storage (FAS) multigrid algorithm implemented in conjunction with three different implicit schemes, which include a modified point Gauss relaxation, a standard Gauss-Seidel line relaxation, and the Beam-Warming alternating direction implicit (ADI) scheme. The flow solver used in the study is based on artificial compressibility and uses a third-order upwind difference for the convective terms and a second-order central difference for the viscous terms. The efficiency of each implicit multigrid scheme is assessed in terms of the computing time required for two laminar flow problems: the entry flow through a 90• bent square duct, and the steady-state and unsteady flows past a prolate spheroid at incidence with an axis ratio of 4 : 1. It is found that implementation of Neumann boundary conditions on the coarse grid in terms of the flow variable correction rather than the flow variable itself is essential for obtaining good convergence in the collocated finite difference discretization. The results of steady-state flow computations show that all the implicit multigrid schemes yield more than 50% computational time savings over their single grid counterparts, and the point or line relaxation multigrid scheme outperforms the ADI multigrid scheme by at least a factor of 2. However, in unsteady flow computations, the computational time saving of the multigrid scheme is less than that in steady-state cases. The current study concludes that the FAS multigrid algorithm implemented with the modified point Gauss relaxation scheme is preferable for simulating both steady-state and time-dependent incompressible flows. c 2002 Elsevier Science (USA)

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Section: Time and Spatial Discretizationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Comparison of Implicit Multigrid Schemes for Three-Dimensional Incompressible Flows

2002

Journal of Computational Physics

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“…The assembling of the coarse grid equation (9) in the described way assures that, for vanishing fine grid residuals R b wh , no corrections DF a H for the fine-grid values are calculated. The term inside the braces depends only on the restricted fine-grid values.…”

Section: Multigrid Methodsmentioning

confidence: 99%

“…Further, Nowak et al [7] extend the coupled solution strategy of Vanka [8] to a multigrid algorithm for laminar flow cases. Another approach, that of Sheng [9], is based on the pseudo-compressibility method of Chorin [10]. This paper describes a finite volume multigrid method (FAS-FMG) for the calculation of turbulent flows in complex three-dimensional geometries.…”

Section: Introductionmentioning

confidence: 99%

Calculation of three-dimensional turbulent flow with a finite volume multigrid method

Cornelius

Volgmann

Stoff

1999

Int. J. Numer. Meth. Fluids

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Finite element solution of free-surface ship-wave problems

Idelsohn

Oñate

Sacco

1999

Int. J. Numer. Meth. Engng.

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SUMMARYAn unstructured ÿnite element solver to evaluate the ship-wave problem is presented. The scheme uses a non-structured ÿnite element algorithm for the Euler or Navier-Stokes ow as for the free-surface boundary problem. The incompressible ow equations are solved via a fractional step method whereas the non-linear free-surface equation is solved via a reference surface which allows ÿxed and moving meshes. A new nonstructured stabilized approximation is used to eliminate spurious numerical oscillations of the free surface.

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Multigrid algorithm for three-dimensional incompressible high-Reynolds number turbulent flows

Cited by 21 publications

References 10 publications

Comparison of Implicit Multigrid Schemes for Three-Dimensional Incompressible Flows

Comparison of Implicit Multigrid Schemes for Three-Dimensional Incompressible Flows

Calculation of three-dimensional turbulent flow with a finite volume multigrid method

Finite element solution of free-surface ship-wave problems

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