On Bi-grid Local Mode Analysis of Solution Techniques for 3-D Euler and Navier–Stokes Equations

Ibraheem, S. O.; Demuren, A. O.

doi:10.1006/jcph.1996.0099

Cited by 7 publications

(5 citation statements)

References 7 publications

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“…The data is determined using matlab's sparse eigenvalue routine to find the largest eigenvalue and hence the slowest decay on a 65×65 grid. This should be more accurate than limited analytical methods such as a bi-grid analysis [3]. Compared with correspondingly simple schemes based upon the usual hierarchy of grids, the method proposed here takes much fewer iterations, even though each iteration is a little more expensive, and so should be about twice as fast.…”

Section: The V-cycle Converges Rapidlymentioning

confidence: 97%

Simple and fast multigrid solution of Poisson's equation using diagonally oriented grids

Roberts¹

2001

ANZIAMJ

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We solve Poisson's equation using new multigrid algorithms that converge rapidly. The novel feature of the 2D and 3D algorithms are the use of extra diagonal grids in the multigrid hierarchy for a much richer and effective communication between the levels of the multigrid. Numerical experiments solving Poisson's equation in the unit square and unit cube show simple versions of the proposed algorithms are up to twice as fast as correspondingly simple multigrid iterations on a conventional hierarchy of grids. *

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Section: The V-cycle Converges Rapidlymentioning

confidence: 97%

Simple and fast multigrid solution of Poisson's equation using diagonally oriented grids

Roberts¹

2001

ANZIAMJ

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“…Both the smoothing factor based on a conventional von Neumann stability analysis and the ampli cation factor based on the bigrid stability analysis are used to study multigrid performance in this work, following Ibraheem and Demuren. 19 The Beam and Warming ADI scheme formulated earlier can be represented in the operator form N Q n L t R n 11…”

Section: Convergence Characteristicsmentioning

confidence: 99%

“…The bigrid ampli cation matrix M is an 8 8 block matrix of which each elemental block is a 5 5 matrix. 19 The eigenvalues for the bigrid matrix M are computed from Eq. (15) over xed Fourier modes to obtain the ampli cation factor.…”

Section: Bigrid Stability Analysismentioning

confidence: 99%

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Multigrid Method for the Euler and Navier-Stokes Equations

Demuren

Ibraheem

1998

AIAA Journal

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Results are presented of a study to implement convergence acceleration techniques based on the multigrid concept in a three-dimensional computer code developed for solving Euler and Navier-Stokes equations. The multigrid method implemented is the full approximation storage-full multigrid algorithm, which is applicable to nonlinear equations. Multigrid convergence estimates based on a single-grid or bigrid stability analysis are performed. The latter was found to yield a better prediction of practical multigrid convergence rates. In typical applications, for both laminar and turbulent ows, savings of up to 50% in CPU time were obtained with the multigrid implementation. Nomenclatureviscous ux vectors e = error vector e 0 = total speci c internal energy g = computational grid in the multigrid sequence I = 1 I H h = restriction operator I h H = interpolation operator I = identity matrix J = transformation Jacobian K = coarse grid correction matrix K L N = Fourier symbols k = turbulent kinetic energy L 1 L 2 L 3 = alternating direction implicit operators M = bigrid ampli cation matrix Ma = Mach number P = forcing term in multigrid procedure p = pressure Q = solution vector R = residual vector Re = Reynolds number R 0 R 1 R 2 S 0 S 1 S 2 = viscous ux Jacobians Y 0 Y 1 Y 2 S 1 S 2 = relaxation or smoothing operator t = time U 0 = constant amplitude vector u = velocity components x y z = Cartesian coordinates = speci c heat capacity ratio = incremental change x y z = nite difference operators = dissipation rate of turbulent kinetic energy i e = coef cients of implicit and explicit arti cial dissipation x y z = Fourier modes in x, y, and z direction = ampli cation factor bg = bigrid ampli cation factor sg = smoothing factor Presented as Paper 96t k t = eddy and thermal viscosity 1 2 = pre-and postrelaxation counters = computational coordinate system = density mg = multigrid convergence factor Subscripts and Superscriptsh H = ne and coarse grid levels n n 1 n 2 = time step or iteration number

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Geometric multigrid with applications to computational fluid dynamics

Wesseling

Oosterlee

2001

Partial Differential Equations

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On Bi-grid Local Mode Analysis of Solution Techniques for 3-D Euler and Navier–Stokes Equations

Cited by 7 publications

References 7 publications

Simple and fast multigrid solution of Poisson's equation using diagonally oriented grids

Simple and fast multigrid solution of Poisson's equation using diagonally oriented grids

Multigrid Method for the Euler and Navier-Stokes Equations

Geometric multigrid with applications to computational fluid dynamics

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