Kernel-based collocation methods for heat transport on evolving surfaces

Meng Chen*, Leevan Ling

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

8 Citations (Scopus)


We propose algorithms for solving convective-diffusion partial differential equations (PDEs), which model surfactant concentration and heat transport on evolving surfaces, based on extrinsic kernel-based meshless collocation methods. The algorithms can be classified into two categories: one collocates PDEs extrinsically and analytically, and the other approximates surface differential operators by meshless pseudospectral approaches. The former is specifically designed to handle PDEs on evolving surfaces defined by parametric equations, and the latter works on surface evolutions based on point clouds. After some convergence studies and comparisons, we demonstrate that the proposed method can solve challenging PDEs posed on surfaces with high curvatures with discontinuous initial conditions with correct physics.

Original languageEnglish
Article number109166
JournalJournal of Computational Physics
Publication statusPublished - 15 Mar 2020

Scopus Subject Areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Convective-diffusion equations
  • Kansa methods
  • Mass conservation
  • Overdetermined formulations
  • Point clouds
  • Radial basis functions


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