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An efficient particle tracking equation with specified spatial step for the solution of the diffusion equation

Chrysikopoulos Constantinos, ScottC.James

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URIhttp://purl.tuc.gr/dl/dias/F7F6A630-5250-4584-9C75-1DF4F3C79AFE-
Identifierhttps://doi.org/10.1016/S0009-2509(01)00344-X -
Languageen-
Extent9 pagesen
TitleAn efficient particle tracking equation with specified spatial step for the solution of the diffusion equationen
CreatorChrysikopoulos Constantinosen
CreatorΧρυσικοπουλος Κωνσταντινοςel
CreatorScottC.Jamesen
Content SummaryThe traditional di(usive particle tracking equation provides an updated particle location as a function of its previous location and molecular di(usion coe cient while maintaining a constant time step. A smaller time step yields an increasingly accurate, yet more computationally demanding solution. Selection of this time step becomes an important consideration and, depending on the complexity of the problem, a single optimum value may not exist. The characteristics of the system under consideration may be such that a constant time step may yield solutions with insu cient accuracy in some portions of the domain and excess computation time for others. In this work, new particle tracking equations speci%cally designed for the solution of problems associated with di(usion processes in one, two, and three dimensions are presented. Instead of a constant time step, the proposed equations employ a constant spatial step. Using a traditional particle tracking algorithm, the travel time necessary for a particle with a di(usion coe cient inversely proportional to its diameter to achieve a pre-speci%ed distance was determined. Because the size of a particle a(ects how it di(uses in a quiescent 8uid, it is expected that two di(erently sized particles would require di(erent travel times to move a given distance. The probability densities of travel times for plumes of monodisperse particles were consistently found to be log-normal in shape. The parameters describing this log-normal distribution, i.e., mean and standard deviation, are functions of the distance speci%ed for travel and the di(usion coe cient of the particles. Thus, a random number selected from this distribution approximates the time required for a given particle to travel a speci%ed distance. The new equations are straightforward and may be easily incorporated into appropriate particle tracking algorithms. In addition, the new particle tracking equations are as accurate and often more computationally e cient than the traditional particle tracking equationen
Type of ItemPeer-Reviewed Journal Publicationen
Type of ItemΔημοσίευση σε Περιοδικό με Κριτέςel
Licensehttp://creativecommons.org/licenses/by/4.0/en
Date of Item2015-09-18-
Date of Publication2001-
Bibliographic CitationS. C.James, C. V. Chrysikopoulos , "An e cient particle tracking equation with speci%ed spatial step for the solution of the diffusion equation ", Chem.Engin. Sc,.vol. 56,no.23 ,pp. 6535–6543, 2001.doi :10.1016/S0009-2509(01)00344-X en

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