Details
| Original language | English |
|---|---|
| Article number | 111310 |
| Journal | Journal of computational physics |
| Volume | 463 |
| Early online date | 18 May 2022 |
| Publication status | Published - 15 Aug 2022 |
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
ASJC Scopus subject areas
- Mathematics(all)
- Numerical Analysis
- Mathematics(all)
- Modelling and Simulation
- Physics and Astronomy(all)
- Physics and Astronomy (miscellaneous)
- Physics and Astronomy(all)
- General Physics and Astronomy
- Computer Science(all)
- Computer Science Applications
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Journal of computational physics, Vol. 463, 111310, 15.08.2022.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - An efficient collocation method for long-time simulation of heat and mass transport on evolving surfaces
AU - Tang, Zhuochao
AU - Fu, Zhuojia
AU - Chen, Meng
AU - Huang, Jingfang
N1 - 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.
PY - 2022/8/15
Y1 - 2022/8/15
N2 - 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.
AB - 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.
KW - Evolving surface
KW - Generalized finite difference method
KW - Krylov deferred correction method
KW - Point clouds
UR - http://www.scopus.com/inward/record.url?scp=85130534690&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2022.111310
DO - 10.1016/j.jcp.2022.111310
M3 - Article
AN - SCOPUS:85130534690
VL - 463
JO - Journal of computational physics
JF - Journal of computational physics
SN - 0021-9991
M1 - 111310
ER -