Calculation of laminar recirculating flows using a local non‐staggered grid refinement system

Coelho, Pedro J.; Pereira, J. C. F.; Carvalho, M. G.

doi:10.1002/fld.1650120603

Cited by 38 publications

(19 citation statements)

References 31 publications

(2 reference statements)

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“…The extension to 3D problems does not present di culties, because the ÿnal form of the discretized equations (19)- (22) remains unchanged and the same is valid for most of the rest modelling expressions, as the cell-face calculation Equations (7) and (8) or the derivatives Equations (9). A little more complex would be the interpolation formulae of Equations (4), (17) and (18) for the auxiliary points deÿnition.…”

Section: Solution Algorithmmentioning

confidence: 96%

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Discretization of transport equations on 2D Cartesian unstructured grids using data from remote cells for the convection terms

Anagnostopoulos

2003

Numerical Methods in Fluids

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SUMMARYThis paper presents a new ÿnite volume discretization methodology for the solution of transport equations on locally reÿned or unstructured Cartesian meshes. The implementation of the cell-face values of the dependent variables enables the employment of data from remote cells and thus the use of higherorder di erencing schemes. It also results in simple and ux-conservative multiple-scale stencils for the discretization of the governing equations. The latter are ÿnally cast into a generalized form that does not depend on the local mesh structure. The performance of the numerical model is demonstrated on some classical 2D problems using various gridding techniques and a bounded second-order upwind scheme. A stable and e cient behaviour of the algorithm is observed in all test cases. The results indicate that the combination in the present model of both local grid reÿnement and second-order discretization can produce substantially more accurate solutions than each of the above techniques alone, for the same computational e ort. The method is also applicable to turbulent ows and can be easily extended to three-dimensions.

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Section: Solution Algorithmmentioning

confidence: 96%

“…In an alternative technique, grid reÿnement algorithms are used to increase the resolution of a base grid at certain regions through cell subdivision [3,[9][10][11][12]. The resulting locally reÿned or embedded grids are usually solved together with the base grid, thus no information transfer is required.…”

Section: Introductionmentioning

confidence: 99%

Discretization of transport equations on 2D Cartesian unstructured grids using data from remote cells for the convection terms

Anagnostopoulos

2003

Numerical Methods in Fluids

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“…The method is particularly suitable for problems with discontinuous properties such as those considered here. [60][61][62] Before the validation and discussion of the results in the next section, here we list the independent non-dimensional parameters governing the physics of the flow under discussion. These are: the fluid properties ratios …”

Section: Implementation Of the Thermal Marangoni Migration Methods mentioning

confidence: 99%

Walls and domain shape effects on the thermal Marangoni migration of three-dimensional droplets

2017

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This version is available at https://strathprints.strath.ac.uk/62121/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output. The thermocapillary motion of liquid droplets in fluid media depends on a variety of influential factors, including the not yet fully understood role played by the presence of the walls and other geometrical constraints. In order to address this specific question, in the present work we rely on a rigorous mathematical and numerical framework (including an adaptive mesh strategy), which are key to perform physically consistent and computationally reliable simulations of such a problem given the different space scales it involves. Our final aim is the proper discernment of the triadic relationship established among viscous phenomena, thermal effects and other specific behaviour due to the proximity of the droplet to a solid boundary. Different geometric configurations are considered (e.g., straight, converging and diverging channels, droplets located near a single or adjacent walls) and distinct regimes are examined (including both (Ma, Re)0 and finite Ma flows). The results show that for straight channels the droplet generally undergoes a decrease in the migration velocity due to its proximity to the wall. Such a departure becomes larger as the Marangoni number is increased. In addition, a velocity component directed perpendicularly to the wall emerges. This effect tends to "pull" the droplet away from the solid boundary if adiabatic conditions are considered, whereas for thermally conducting sidewalls and relatively large values of the Marangoni number, the distortion of the temperature field in the region between the droplet and the wall results in a net force with a component directed towards the surface. For non-straight channels, the dynamics depend essentially on the balance between two counteracting factors, namely, the effective distribution of temperature established in the channel (for which we provide a...

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“…Other authors couple reÿned and non-reÿned regions at the same level, computing the whole grid simultaneously [23][24][25][26][27][28]. Special discretisation schemes are required for the coarse-ÿne grid transition.…”

Section: Introductionmentioning

confidence: 98%

Local block refinement with a multigrid flow solver

Lange

Schäfer

Durst

2001

Numerical Methods in Fluids

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SUMMARYA local block reÿnement procedure for the e cient computation of transient incompressible ows with heat transfer is presented. The procedure uses patched structured grids for the blockwise reÿnement and a parallel multigrid ÿnite volume method with colocated primitive variables to solve the NavierStokes equations. No restriction is imposed on the value of the reÿnement rate and non-integer rates may also be used. The procedure is analysed with respect to its sensitivity to the reÿnement rate and to the corresponding accuracy. Several applications exemplify the advantages of the method in comparison with a common block structured grid approach. The results show that it is possible to achieve an improvement in accuracy with simultaneous signiÿcant savings in computing time and memory requirements.

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Calculation of laminar recirculating flows using a local non‐staggered grid refinement system

Cited by 38 publications

References 31 publications

Discretization of transport equations on 2D Cartesian unstructured grids using data from remote cells for the convection terms

Discretization of transport equations on 2D Cartesian unstructured grids using data from remote cells for the convection terms

Walls and domain shape effects on the thermal Marangoni migration of three-dimensional droplets

Local block refinement with a multigrid flow solver

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