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 -