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DOI: 10.1615/ICHMT.2008.CHT.360
22 pages

Carmine Golia
Department of Aerospace and Mechanical Engineering, Faculty of Engineering, Second University of Naples, via Roma 29, 81031 Aversa, Italy

Bernardo Buonomo
Dipartimento di Ingegneria Industriale e dell'Informazione, Università degli Studi della Campania "Luigi Vanvitelli," Aversa (CE), Italy

Antonio Viviani
Seconda Università di Napoli


To improve the accuracy of both the integral approximation of differential operators (Divergence, Gradient and Laplacian) and of the regrid process, in the simulation of 3D thermal buoyant flows with meshless Lagrangian Blobs methods, the authors developed an integral discretization of the differential operators of the field equations, by using convolutions of truncated 3D-Taylor series expansions of field functions with a kernel defined on a compact domain around the blob centre of a given particle (Taylor Convolution Complete: TCC). This method allows to overtake the irregular distribution of cells in the compact domain around the given blob, the deficiency of cells in the compact support due to the presence of a boundaries cutting the compact support of nearby blobs, and allows to delay the use of regrid process to smooth the blob spatial distribution. The main scope of the present work is to explore new higher order kernels capable to give an accuracy larger than the classical one [O(h2)]. They propose a new polynomial kernel that is used within TCC to compute Gradients, Laplacian terms and for regrid processes. This new formulation, that is [O(h3)], is verified by solving a plume thermal buoyant problem, at realistic values of the Grashof number [O(1010)], and compared with the same problem solved with classical kernel. The use of new kernel gives much better results: larger rising of the plume and better time trends of the control parameter than are within 2 orders of magnitude smaller. Due to the better accuracy and details, the time trend of the global zeroth order vorticity Moment presents two spikes that are investigated in details. The first event is found to correspond to a pinch-off phenomenon between stem and cap of the trailing buoyant mushroom and is verified at a non-dimensional time that falls within the interval limit stated by theoretical and experimental findings available in the literature. The second event is also dependent by secondary pinch-off phenomenon that is verified within the mushroom cap, but up to now relating experimental evidences are not available in the literature.

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