{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:33:44Z","timestamp":1787337224499,"version":"build-2736575974"},"reference-count":9,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>In this paper we improve the numerical schemes presented in a recent publication by Qamar and Warnecke [Chem. Eng. Sci., 31 (2007), pp. 1576\u20131589]. It is observed that the proposed numerical schemes do not preserve certain required moments of size distributions. In this paper, slightly different formulations are given that preserve these moments. The new formulations are compared with the old formulations by the application of three analytically solvable problems. It is shown that the new formulations are very accurate for predicting number density distributions as well as certain moments. While the old formulations are accurate enough for predicting the number density distribution, they show peculiar behavior for certain moments.<\/jats:p>","DOI":"10.1137\/090757356","type":"journal-article","created":{"date-parts":[[2010,3,3]],"date-time":"2010-03-03T18:09:18Z","timestamp":1267639758000},"page":"703-713","source":"Crossref","is-referenced-by-count":12,"title":["A Note on Moment Preservation of Finite Volume Schemes for Solving Growth and Aggregation Population Balance Equations"],"prefix":"10.1137","volume":"32","author":[{"given":"Jitendra","family":"Kumar","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gerald","family":"Warnecke","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,3,3]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827503429132"},{"key":"R2","doi-asserted-by":"crossref","unstructured":"R. J. LeVeque,\n                      Finite Volume Methods for Hyperbolic Problems\n                      , Cambridge University Press, Cambridge, UK, 2002.","DOI":"10.1017\/CBO9780511791253"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/S0009-2509(97)00307-2"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/j.compchemeng.2007.01.006"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(74)90019-9"},{"key":"R6","doi-asserted-by":"crossref","unstructured":"L. M\u00f6rl, S. Heinrich, and M. Peglow,\n                      Fluidized bed spray granulation\n                      , in Handbook of Powder Technology, 11, 2006, pp. 21\u2013188.","DOI":"10.1016\/S0167-3785(07)80037-6"},{"key":"R7","unstructured":"D. Ramkrishna,\n                      Population Balances\n                      , Academic Press, New York, 2000."},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1016\/j.ces.2005.12.014"},{"key":"R9","doi-asserted-by":"crossref","unstructured":"J. Kumar, M. Peglow, G. Warnecke, and S. Heinrich,\n                      An efficient numerical technique for solving population balance equation involving aggregation, breakage, growth and nucleation\n                      Powder Technology, 182, pp. 81\u2013104.","DOI":"10.1016\/j.powtec.2007.05.028"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/090757356","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:50:12Z","timestamp":1787334612000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/090757356"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":9,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1137\/090757356"],"URL":"https:\/\/doi.org\/10.1137\/090757356","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1]]}}}