A Green's discrete transformation meshfree method for simulating transient diffusion problems

Weijie Mai, Soheil Soghrati, Rudolph G. Buchheit

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


This manuscript presents the formulation and application of the Green's discrete transformation method (GDTM) for the meshfree simulation of transient diffusion problems, including those with moving boundaries. The GDTM implements a linear combination of time-dependent Green's basis functions defined on a set of source points to approximate the field in the form of a solution series. A discrete transformation is implemented to evaluate unknown coefficients of this series, which eliminates the need to use time integration schemes. We will study the optimal number and location of the GDTM source points that yield the highest level of accuracy, while maintaining a manageable condition number for the resulting linear system of equations. The optimal values of these parameters, which are inherently independent of the domain geometry, are determined such that the basis functions have appropriate features for approximating the field. A comprehensive convergence study is presented to show the precision and convergence rate of the GDTM for modeling various diffusion problems. We also demonstrate the application of this method for simulating three diffusion problems with complex and evolving morphologies: heat transfer in a turbine blade, thermal response of a porous material, and localized (pitting) corrosion in stainless steel.

Original languageEnglish
Pages (from-to)252-270
Number of pages19
JournalInternational Journal for Numerical Methods in Engineering
Issue number3
StatePublished - Oct 19 2016

Bibliographical note

Publisher Copyright:
Copyright © 2016 John Wiley & Sons, Ltd.


  • Green's function
  • heat transfer
  • meshfree method
  • moving boundary
  • pitting corrosion
  • transient diffusion

ASJC Scopus subject areas

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics


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