Multigrid pressure correction techniques for the computation of quasi‐incompressible internal flows

Luchini, Paolo; D'Alascio, A.

doi:10.1002/fld.1650180505

Cited by 6 publications

(6 citation statements)

References 12 publications

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“…This is very simple and its smoothing properties are as good as any other's for the present problem. In a classical full multigrid V-cycle the smoothing factor of red-black is of the order of 3, meaning that the error norm is reduced by a factor of approximately 3 for each complete cycle, but this factor can be increased to 9 with the modification proposed in Luchini & D'Alascio (1994), to which we refer for a description of the algorithm with application to the solution of the Poisson equation in a structured Cartesian…”

Section: Boundary Conditionsmentioning

confidence: 99%

The start-up vortex issuing from a semi-infinite flat plate

Luchini

Tognaccini

2002

J. Fluid Mech.

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The subject of the present work is the start-up vortex issuing from a sharp trailing edge accelerated from rest in still air. A numerical simulation of the flow has been performed in the case of a semi-infinite flat plate by solving the Navier-Stokes equations in the psi-omega formulation. The numerical algorithm is based on a fast multigrid implicit integration of the difference equations in an unstructured mesh that is dynamically built to minimize the computational costs. A local refinement of the mesh near the edge of the plate increases the accuracy of the simulation. The results show that the asymptotic stage of the vortex evolution is self-similar in the mean, but the appearance of instabilities produces a time-dependent flow which is not instantaneously self-similar

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Section: Boundary Conditionsmentioning

confidence: 99%

The start-up vortex issuing from a semi-infinite flat plate

Luchini

Tognaccini

2002

J. Fluid Mech.

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“…This is very simple and its smoothing properties are equivalent to any other's for the present problem. In a classical full multigrid V-cycle the smoothing factor of red-black is of the order of 1/3 meaning that the error norm is reduced by a factor of approximately 1/3 for each complete cycle, but this factor can be increased to 1/9 with the modification proposed in [12] to which we refer for a description of the algorithm with application to the solution of the Poisson equation in a structured cartesian mesh. The convergence speed improvement is essentially due to a modification of the restriction stage with the available residual on the finer grid which is equivalent to an additional red-black smoothing.…”

mentioning

confidence: 99%

Comparison of viscous and inviscid numerical simulations of the start-up vortex issuing from a semi-infinite flat plate

Luchini

Tognaccini²

1999

ESAIM: Proc.

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Subject of the present work is the start-up vortex issuing from a sharp trailing edge accelerated from rest in still air. A numerical simulation of the flow has been performed in case of a semi-infinite flat plate by solving the Navier-Stokes equations in the ψ−ω formulation. The new numerical algorithm is based on a fast multigrid implicit integration of the difference equations in an unstructured mesh that is dynamically built to minimize the computational costs. The results, compared with inviscid lumped-vortex simulations, show the appearance of instabilities that quickly destroy

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“…37 The multigrid method has been applied to PISO, again for a combustion chamber application. 38 Dukowicz 39 presented an example of particulate time-dependent¯ow with a Monte Carlo simulation for particle dispersion.…”

Section: Scheme 4 Pisomentioning

confidence: 99%

Comparison of SIMPLE- and PISO-type algorithms for transient flows

Barton

1998

Int. J. Numer. Meth. Fluids

119

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Various pressure‐based schemes are proposed for transient flows based on well‐established SIMPLE and PISO algorithms. The schemes are applied to the solution of unsteady laminar flow around a square cylinder and steady laminar flow over a backward‐facing step. The implicit treatment and the performance of the various schemes are evaluated by using benchmark solutions with a small time step. Three different second‐order‐accurate time derivatives based on different time levels are presented. The different time derivatives are applied to the various schemes under consideration. Overall the PISO scheme was found to predict accurate results and was robust. However, for small time step values, alternative schemes can predict accurate results for approximately half the computational cost. The choice of time derivative proved to be very significant in terms of the accuracy and robustness of a scheme. Significantly, the one‐sided forward differencing scheme was the most successful used in conjunction with a strongly implicit‐based algorithm. However, a greater degree of accuracy was achieved using the standard PISO algorithm with the Crank–Nicolson time derivative. Recommendations for future work are discussed. © 1998 John Wiley & Sons, Ltd.

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Multigrid pressure correction techniques for the computation of quasi‐incompressible internal flows

Cited by 6 publications

References 12 publications

The start-up vortex issuing from a semi-infinite flat plate

The start-up vortex issuing from a semi-infinite flat plate

Comparison of viscous and inviscid numerical simulations of the start-up vortex issuing from a semi-infinite flat plate

Comparison of SIMPLE- and PISO-type algorithms for transient flows

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