An efficient collocation method for long-time simulation of heat and mass transport on evolving surfaces

authored by: Zhuochao Tang, Zhuojia Fu, Meng Chen, Jingfang Huang
Abstract: This paper presents an efficient collocation method which combines the generalized finite difference method (GFDM) with the Krylov deferred correction (KDC) method for the long-time simulation of heat and mass transport on evolving surfaces. The KDC method utilizes a pseudo-spectral-type temporal collocation formulation to discretize the time-dependent surface heat and mass transport equation in each time marching step, where the time derivatives at the collocation points are introduced as the new unknown variables. A low-order time marching scheme is then applied as an effective preconditioner in the Jacobian-Free Newton-Krylov framework to decouple the spatial surface PDEs at different collocation nodes. Each decoupled surface PDE is then solved by the meshless GFDM, where both the continuous-form evolving surfaces defined by parametric equations and discretized-form evolving surfaces composed of point clouds are considered in the GFDM spatial discretization. Numerical experiments show that the combined GFDM-KDC solver is a promising numerical scheme for long-time evolution simulation of heat and mass transport on intractable evolving surfaces.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Hohai University
Nanjing University of Aeronautics and Astronautics
Nanchang University
University of North Carolina
Type: Article
Journal: Journal of computational physics
Volume: 463
ISSN: 0021-9991
Publication date: 15.08.2022
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Numerical Analysis, Modelling and Simulation, Physics and Astronomy (miscellaneous), General Physics and Astronomy, Computer Science Applications, Computational Mathematics, Applied Mathematics
Electronic version(s): https://doi.org/10.1016/j.jcp.2022.111310 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{6fa645511d6540a3b63c17187ff19ed2,
title = "An efficient collocation method for long-time simulation of heat and mass transport on evolving surfaces",
abstract = "This paper presents an efficient collocation method which combines the generalized finite difference method (GFDM) with the Krylov deferred correction (KDC) method for the long-time simulation of heat and mass transport on evolving surfaces. The KDC method utilizes a pseudo-spectral-type temporal collocation formulation to discretize the time-dependent surface heat and mass transport equation in each time marching step, where the time derivatives at the collocation points are introduced as the new unknown variables. A low-order time marching scheme is then applied as an effective preconditioner in the Jacobian-Free Newton-Krylov framework to decouple the spatial surface PDEs at different collocation nodes. Each decoupled surface PDE is then solved by the meshless GFDM, where both the continuous-form evolving surfaces defined by parametric equations and discretized-form evolving surfaces composed of point clouds are considered in the GFDM spatial discretization. Numerical experiments show that the combined GFDM-KDC solver is a promising numerical scheme for long-time evolution simulation of heat and mass transport on intractable evolving surfaces.",
keywords = "Evolving surface, Generalized finite difference method, Krylov deferred correction method, Point clouds",
author = "Zhuochao Tang and Zhuojia Fu and Meng Chen and Jingfang Huang",
note = "Funding Information: The authors thank the reviewers for their insightful suggestions which make the paper of better quality. This work was supported by the National Science Foundation of China (Grant No. 12122205 , No. 12001261 ), Fundamental Research Funds for the Central Universities (Grant No. B220203018 ), Alexander von Humboldt Research Fellowship (ID: 1195938 ), Six Talent Peaks Project in Jiangsu Province of China (Grant No. 2019-KTHY-009 ) and the Jiangxi Provincial Natural Science Foundation (Grant No. 20212BAB211020 ). Part of the work was done when Z. Tang was a visiting scholar at the University of North Carolina at Chapel Hill. ",
year = "2022",
month = aug,
day = "15",
doi = "10.1016/j.jcp.2022.111310",
language = "English",
volume = "463",
journal = "Journal of computational physics",
issn = "0021-9991",
publisher = "Academic Press Inc.",
}