Stretched Cartesian grids for solution of the incompressible Navier-Stokes equations

Avital, Eldad; Sandham, Neil D.; Luo, Kai

doi:10.1002/1097-0363(20000730)33:6<897::aid-fld37>3.0.co;2-4

Cited by 15 publications

(9 citation statements)

References 20 publications

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“…The present mapping is a generalization of those proposed by [4] and [3]. It preserves the accuracy while avoiding the expensive computation of a full convolution and ensuring the strict physical/spectral equivalence.…”

Section: Extension Toward a Stretched Mesh In One Directionmentioning

confidence: 93%

“…However, the condition required to obtain such a favourable behaviour is that the function submitted to the differentiation must verify the boundary conditions (36). 3 The drawback of ghost boundary conditions (16) is that they limit any scheme to the second-order accuracy, but their important advantage is that they allow the discretization to remain homogeneous in the whole computational domain. Then, it is possible to define exactly and easily the differentiation in spectral space.…”

Section: Extension Toward Homogeneous Neumann Conditionsmentioning

confidence: 99%

“…For instance, the simple solving of the Poisson equation based only on a single division in spectral space is lost. However, following the stretching technique introduced by [4] and extended by [3], a slight modification of the Poisson solver is proposed, based on a specific function mapping and expressed using only few Fourier modes. Thus, the spectral and non-iterative nature of the pressure treatment can be preserved without significant loss of accuracy.…”

Section: Extension Toward a Stretched Mesh In One Directionmentioning

confidence: 99%

“…(54) degenerates to Cain et al's [4] mapping function that leads to a fine mesh in the centre of an infinite domain L y ¼ 1. For a -0, c ¼ 1 and d ¼ 0, present function corresponds to the one of [3] that allows a central mesh refinement in a finite domain. Using c ¼ 1 and d ¼ 1=2, the concentration of mesh nodes is performed near the boundaries of the domain at y ¼ 0 and L y .…”

Section: Extension Toward a Stretched Mesh In One Directionmentioning

confidence: 99%

See 3 more Smart Citations

High-order compact schemes for incompressible flows: A simple and efficient method with quasi-spectral accuracy

Laizet

Lamballais

2009

Journal of Computational Physics

311

205

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Section: Extension Toward a Stretched Mesh In One Directionmentioning

confidence: 93%

Section: Extension Toward Homogeneous Neumann Conditionsmentioning

confidence: 99%

Section: Extension Toward a Stretched Mesh In One Directionmentioning

confidence: 99%

Section: Extension Toward a Stretched Mesh In One Directionmentioning

confidence: 99%

See 2 more Smart Citations

High-order compact schemes for incompressible flows: A simple and efficient method with quasi-spectral accuracy

Laizet

Lamballais

2009

Journal of Computational Physics

311

205

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“…directions, yielding a ratio of 2:1 between the spacing at the outer edge to that at the centre of the computational domain. The type of the grid mapping is the same as used in Avital et al [24]. The computational domain was of the size of (50, 30, 30)R e , where R e is the initial effective radius of the jet.…”

Section: Hydrodynamic and Acoustic Formulations 21 Hydrodynamic Formentioning

confidence: 99%

Study of Sound Generated by Large-Scale Structures in Low Speed Coaxial Jets

Alonso¹,

Avital

2009

International Journal of Aeroacoustics

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Sound generation by low speed circular and elliptic coaxial jets is investigated computationally. The secondary to primary jet velocity ratio is limited up to 0.4 and the elliptic jet profile has a 2:1 aspect ratio. Large Eddy Simulations are coupled with the Lighthill's acoustic analogy. Flow incompressibility is assumed limiting the study to the compact quadrupole structures generated during the jet mixing process. As expected, adding a secondary stream is found to extend the mixing region, while changing the jet geometry from circular to elliptic leads to vice versa. Good qualitative agreement in the flow behaviour is achieved with known results. Lighthill's longitudinal streamwise quadrupole is found to dominate the sound generation leading to a mildly high streamwise emission. Increasing the velocity ratio of the secondary stream to the primary stream increases the dominance of the streamwise sound emission. Good qualitative agreement with a previously suggested sound directivity pattern is achieved. Adding a secondary stream to the jet is found to have a mixed effect on the emitted acoustic power. A plausible explanation based on a large scale instability wave model is presented. Dominance of the longitudinal streamwise quadrupole Qxx was observed in all jets and the lateral quadrupoles Qxy and Qxz were of about the same magnitude and only secondary to Qxx. This resulted in high sound emission in the streamwise direction particularly as U1 /U0 was increased to 0.4. Good qualitative agreement was found with a previously suggested expression for the sound directivity pattern [18]. Adding a secondary stream did not cause a significant reduction in the overall acoustic power output as changing the jet geometry from circular to elliptic which was also limited to about 2 dB reduction. Further evidence for the existence of a large scale wave packet structure in the mixing region was produced. The wave packet source model was used to point to the opposing effects on the acoustic power output when adding a secondary stream, which could result in its mild and mixed effect.

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Incompact3d: A powerful tool to tackle turbulence problems with up to O(10⁵) computational cores

Laizet

2010

Numerical Methods in Fluids

183

132

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SUMMARYUnderstanding the nature of complex turbulent flows remains one of the most challenging problems in classical physics. Significant progress has been made recently using high performance computing, and computational fluid dynamics is now a credible alternative to experiments and theories in order to understand the rich physics of turbulence. In this paper, we present an efficient numerical tool called Incompact3d that can be coupled with massive parallel platforms in order to simulate turbulence problems with as much complexity as possible, using up to O(10 5 ) computational cores by means of direct numerical simulation (DNS). DNS is the simplest approach conceptually to investigate turbulence, featuring the highest temporal and spatial accuracy and it requires extraordinary powerful resources. This paper is an extension of Laizet et al.

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Stretched Cartesian grids for solution of the incompressible Navier-Stokes equations

Cited by 15 publications

References 20 publications

High-order compact schemes for incompressible flows: A simple and efficient method with quasi-spectral accuracy

High-order compact schemes for incompressible flows: A simple and efficient method with quasi-spectral accuracy

Study of Sound Generated by Large-Scale Structures in Low Speed Coaxial Jets

Incompact3d: A powerful tool to tackle turbulence problems with up to O(10⁵) computational cores

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Stretched Cartesian grids for solution of the incompressible Navier-Stokes equations

Cited by 15 publications

References 20 publications

High-order compact schemes for incompressible flows: A simple and efficient method with quasi-spectral accuracy

High-order compact schemes for incompressible flows: A simple and efficient method with quasi-spectral accuracy

Study of Sound Generated by Large-Scale Structures in Low Speed Coaxial Jets

Incompact3d: A powerful tool to tackle turbulence problems with up to O(105) computational cores

Contact Info

Product

Resources

About

Incompact3d: A powerful tool to tackle turbulence problems with up to O(10⁵) computational cores