2013
DOI: 10.1108/09615531311289187
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Solution of a low Prandtl number natural convection benchmark by a local meshless method

Abstract: Purpose-Solution of a highly nonlinear fluid dynamics in a low Prandtl number regime, typical for metal like materials, as defined in the Call for contributions to a numerical benchmark problem for 2D columnar solidification of binary alloys (Bellet, et al., 2009). The solution of such a numerical situation represents the first steps towards understanding the instabilities in a more complex case of macrosegregation. Approach-The involved temperature, velocity and pressure fields are represented through the loc… Show more

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Cited by 32 publications
(25 citation statements)
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“…The obtained steady state flow patterns and temperature distribution are depicted in Figure 10 for the following Rayleigh numbers Ra ¼ 10 3 , 10 4 , 10 5 , 10 6 , 10 7 and 10 8 . These results, obtained with a mesh of 142 Â 142, are in good agreements with the results of Kosec and Šarler (2013) using a mesh of (101 Â 101), those of Mayne et al (2000) using the h-adaptive finite element solution and those of Wan et al (2001) using a mesh of 301 Â 301. For this test problem, the Nusselt number is of particular interest since it measures the amount of heat transferred between the plates.…”
Section: The De Vahl Davis Benchmarksupporting
confidence: 85%
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“…The obtained steady state flow patterns and temperature distribution are depicted in Figure 10 for the following Rayleigh numbers Ra ¼ 10 3 , 10 4 , 10 5 , 10 6 , 10 7 and 10 8 . These results, obtained with a mesh of 142 Â 142, are in good agreements with the results of Kosec and Šarler (2013) using a mesh of (101 Â 101), those of Mayne et al (2000) using the h-adaptive finite element solution and those of Wan et al (2001) using a mesh of 301 Â 301. For this test problem, the Nusselt number is of particular interest since it measures the amount of heat transferred between the plates.…”
Section: The De Vahl Davis Benchmarksupporting
confidence: 85%
“…Figure 12 shows the time evolution of the average Nusselt number at the hot wall using three meshes of, respectively, 250,000, 320,000 and 500,000 triangles. This figure shows complicated periodic oscillations of the Nusselt number as has been observed by Kosec and Šarler (2013). The three meshes lead to close final periods of oscillations with small phase shifts.…”
Section: The Periodic Oscillatory Flow For Low Prandtl Numbersupporting
confidence: 71%
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“…The simulations were left to converge to a steady state, characterized by the stopping criteria -temperature change between two consecutive time steps is lower than 0.01% in all nodes -or to run for a limited amount of time and then return an infeasible result, assuming the natural convection resulted in either chaotic or periodical solution [28]. The non-stationary solutions are excluded from consideration.…”
Section: Resultsmentioning
confidence: 99%