2020
DOI: 10.1016/j.matcom.2019.12.009
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Finite volume approximation of multidimensional aggregation population balance equation on triangular grid

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Cited by 16 publications
(12 citation statements)
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“…Furthermore, the Monte Carlo method developed by Matsoukas and Marshall 48 shows deviation from the theoretical result even though the numerical simulations are run using 10000 particles in the system (computationally expensive). During the recent developments, Singh et al 40,49 have shown that changing the grid type from rectangular to structured triangular grid (400 nonuniform cells) and unstructured triangular grids (625 nonuniform cells) improve the variance of excess solute parameter χ2 to certain extent. This shows that the existing scheme consumed large number of grids to achieve the accuracy but a computational expense.…”
Section: Numerical Testing and Discussionmentioning
confidence: 99%
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“…Furthermore, the Monte Carlo method developed by Matsoukas and Marshall 48 shows deviation from the theoretical result even though the numerical simulations are run using 10000 particles in the system (computationally expensive). During the recent developments, Singh et al 40,49 have shown that changing the grid type from rectangular to structured triangular grid (400 nonuniform cells) and unstructured triangular grids (625 nonuniform cells) improve the variance of excess solute parameter χ2 to certain extent. This shows that the existing scheme consumed large number of grids to achieve the accuracy but a computational expense.…”
Section: Numerical Testing and Discussionmentioning
confidence: 99%
“…Existing finite volume scheme 23 verified their numerical results, specifically first‐ and second‐order moments along with number density function for only size‐independent kernel. Moreover, no account has been taken for the accurate prediction of the third‐order moments which play very important role in predicting the skewness of the distribution functions 26,40 . Even to achieve a higher accuracy for the first‐ and second‐order moments, a very refined grid of 1600 nonuniform cells is considered which makes the mathematical formulation less efficient and consumes more time to calculate the numerical results.…”
Section: Numerical Testing and Discussionmentioning
confidence: 99%
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“…Therefore, in this exercise, we choose numerical approximations to solve bivariate pure aggregation PBE (1). To date, many numerical methods have been proposed by various authors, including fixed pivot techniques [24][25][26], method of projection [27], Euler method [28], finite volume schemes [29][30][31][32][33][34][35][36][37][38][39], quadrature method of moments [40][41][42][43], finite element method [44,45], sectional methods [18,[46][47][48][49][50] and Monte Carlo method [19,[51][52][53]. Among all numerical schemes, the cell average technique (CAT) is well known for the accurate prediction of the number distribution function and their moments.…”
Section: Introductionmentioning
confidence: 99%
“…This significantly shows that the orientation and directionality of the grid plays significant role in predicting the various results accurately. However, the applications of the finite volume scheme are only limited to rectangular and triangular grids [36]. The triangular grid is generated by the slicing rectangular grid along the diagonal as shown in Fig.…”
Section: Introductionmentioning
confidence: 99%