A hybrid scheme of single relaxation time lattice Boltzmann and finite volume methods coupled with discrete ordinates method for combined natural convection and volumetric radiation in an enclosure
JOURNAL OF COMPUTATIONAL APPLIED MECHANICS
Authors: Soualmi, Rabiaa; Benbrik, Abderrahmane; Lemonnier, Denis; Cherifi, Mohammed; Bouanani, Mohammed
Abstract
This paper is focused on the application of hybrid Single relaxation time lattice Boltzmann and finite volume methods in conjunction with discrete ordinates method to simulate coupled natural convection and volumetric radiation in differentially heated enclosure, filled with an absorbing, emitting and non-scattering gray medium. In this work, the velocity and temperature fields are calculated using lattice Boltzmann and finite volume methods respectively, whereas the radiative term is computed by the discrete ordinates method. This study is carried out for Pr = 0.71, a Rayleigh number range of 10(3) <= Ra <= 10(6), an optical thickness with values 0 <= tau <= 100, a Planck number ranging in 0.001 <= Pl <= 100 and an aspect ratio varying between 0.5 <= Ar <= 2. Results are presented in terms of streamlines, isotherms, velocity profiles and average Nusselt number. Based on the obtained results, it can be concluded that the presence of volumetric radiation is noteworthy. Its effect, as a function of Rayleigh number and the radiative properties, yields significant changes on the behavior of streamlines and isotherms. In the taller enclosure, the increase of average total Nusselt number with increasing Rayleigh number is less significant than that in the case of the shallow enclosure.
Pattern-avoiding permutation powers
DISCRETE MATHEMATICS
Authors: Burcroff, Amanda; Defant, Colin
Abstract
Recently, Bona and Smith defined strong pattern avoidance, saying that a permutation pi strongly avoids a pattern tau if pi and pi(2) both avoid tau. They conjectured that for every positive integer k, there is a permutation in S-k3 that strongly avoids 123 ... (k+1). We use the Robinson-Schensted-Knuth correspondence to settle this conjecture, showing that the number of such permutations is at least k(k3/2+O(k3/log k)) and at most k(2k3+O(k3/log k)). We enumerate 231-avoiding permutations of order 3, and we give two further enumerative results concerning strong pattern avoidance. We also consider permutations whose powers all avoid a pattern tau. Finally, we study subgroups of symmetric groups whose elements all avoid certain patterns. This leads to several new open problems connecting the group structures of symmetric groups with pattern avoidance. (C) 2020 Elsevier B.V. All rights reserved.
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