Extension and convergence analysis of the univariate direct quadrature spanning tree method

The univariate direct quadrature spanning tree (DQST) method was evaluated with respect to accuracy and computational cost. This included a convergence analysis over the discretization of the breakage term and an accuracy analysis of the smoothing procedure. We also proposed many enhancements to the...

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Bibliographic Details
Published in:Powder technology 2017-12, Vol.322, p.301-313
Main Authors: Ferreira, Gabriel G.S., Lage, Paulo L.C., Silva, Luiz Fernando L.R.
Format: Article
Language:English
Subjects:
Accuracy
Aggregation
Breakage
Computational efficiency
Computer applications
Convergence
Cost analysis
Data smoothing
Distribution
Growth
Integration
Moving pivot
Numerical methods
Population balance
Smoothing
Time integration
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Summary:The univariate direct quadrature spanning tree (DQST) method was evaluated with respect to accuracy and computational cost. This included a convergence analysis over the discretization of the breakage term and an accuracy analysis of the smoothing procedure. We also proposed many enhancements to the method, including a second-order time integration scheme, a new initialization method and its extension for cases involving growth. We have shown that the original smoothing procedure does not conserve the second-order moment of the distribution. In order to guarantee its conservation, a new smoothing method was proposed. The usage of the new smoothing method combined with the second-order time integration scheme reduced the moment errors by several orders of magnitude with a modest increase in the computational cost. [Display omitted] •The differential formulation of the DQST method allowed 2nd order time integration.•A new second-order moment conservative smoothing procedure is proposed.•The DQST method was extended for the solution of problems involving growth.•The enhanced DQST method is much more accurate with a modest increase in its cost.•The convergence order of the enhanced method was verified to be between 0.5 and 1.6.
ISSN:0032-5910
1873-328X
DOI:10.1016/j.powtec.2017.09.017