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Hybrid quadrature moment method for accurate and stable representation of non-Gaussian processes applied to bubble dynamics

Charalampopoulos, A. and Bryngelson, S. H. and Colonius, T. and Sapsis, T. P. (2022) Hybrid quadrature moment method for accurate and stable representation of non-Gaussian processes applied to bubble dynamics. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences, 380 (2229). Art. No. 20210209. ISSN 1364-503X. doi:10.1098/rsta.2021.0209.

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Solving the population balance equation (PBE) for the dynamics of a dispersed phase coupled to a continuous fluid is expensive. Still, one can reduce the cost by representing the evolving particle density function in terms of its moments. In particular, quadrature-based moment methods (QBMMs) invert these moments with a quadrature rule, approximating the required statistics. QBMMs have been shown to accurately model sprays and soot with a relatively compact set of moments. However, significantly non-Gaussian processes such as bubble dynamics lead to numerical instabilities when extending their moment sets accordingly. We solve this problem by training a recurrent neural network (RNN) that adjusts the QBMM quadrature to evaluate unclosed moments with higher accuracy. The proposed method is tested on a simple model of bubbles oscillating in response to a temporally fluctuating pressure field. The approach decreases model-form error by a factor of 10 when compared with traditional QBMMs. It is both numerically stable and computationally efficient since it does not expand the baseline moment set. Additional quadrature points are also assessed, optimally placed and weighted according to an additional RNN. These points further decrease the error at low cost since the moment set is again unchanged.

Item Type:Article
Related URLs:
URLURL TypeDescription
Charalampopoulos, A.0000-0003-4136-0363
Bryngelson, S. H.0000-0003-1750-7265
Colonius, T.0000-0003-0326-3909
Sapsis, T. P.0000-0003-0302-0691
Additional Information:© 2022 The Author(s). Published by the Royal Society. Manuscript received15/09/2021. Manuscript accepted07/01/2022. Published online20/06/2022. Published in print08/08/2022. This article is part of the theme issue ‘Data-driven prediction in dynamical systems’. The authors thank Rodney Fox and Alberto Passalacqua for valuable discussion of quadrature moment methods. The US Office of Naval Research supported this work under grant nos. N0014-17-1-2676 and N0014-18-1-2625. Computations were performed via the Extreme Science and Engineering Discovery Environment (XSEDE) under allocation CTS120005, supported by National Science Foundation grant no. ACI-1548562. We declare we have no competing interests.
Funding AgencyGrant Number
Office of Naval Research (ONR)N0014-17-1-2676
Office of Naval Research (ONR)N0014-18-1-2625
Issue or Number:2229
Record Number:CaltechAUTHORS:20220725-156674000
Persistent URL:
Official Citation:Charalampopoulos A., Bryngelson S. H., Colonius T. and Sapsis T. P. 2022Hybrid quadrature moment method for accurate and stable representation of non-Gaussian processes applied to bubble dynamicsPhil. Trans. R. Soc. A. 380 20210209 20210209
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:115827
Deposited By: George Porter
Deposited On:27 Jul 2022 16:27
Last Modified:27 Jul 2022 16:27

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