Treatment of material discontinuity in two meshless local Petrov-Galerkin (MLPG) formulations of axisymmetric transient heat conduction

R. C. Batra, Maurizio Porfiri, D. Spinello

Research output: Contribution to journalArticle

Abstract

We use two meshless local Petrov-Galerkin (MLPG) formulations to analyse a heat conduction in a bimetallic circular disk. The continuity of the normal component of the heat flux at the interface between two materials is satisfied either by the method of Lagrange multipliers or by using a jump function. The convergence of the H0 and H1 error norms for the four numerical solutions with an increase in the number of equally spaced nodes and in the number of quadrature points is scrutinized. With an increase in the number of uniformly spaced nodes, the two error norms decrease monotonically for the MLPG5 formulation bur are essentially unchanged for the MLPG1 formulation. To our knowledge, this is the first study comparing the performance of the two methods of modelling a discontinuity in the gradient of a field variable at the interface between two different materials.

Original languageEnglish (US)
Pages (from-to)2461-2479
Number of pages19
JournalInternational Journal for Numerical Methods in Engineering
Volume61
Issue number14
DOIs
StatePublished - Dec 14 2004

Fingerprint

Transient Heat Conduction
Petrov-Galerkin
Meshless
Heat conduction
Discontinuity
Formulation
Lagrange multipliers
Norm
Heat flux
Vertex of a graph
Heat Conduction
Heat Flux
Quadrature
Jump
Numerical Solution
Gradient
Decrease
Modeling

Keywords

  • Convergence studies
  • Jump function
  • Lagrange multipliers
  • Meshless MLPG1 and MLPG5 methods

ASJC Scopus subject areas

  • Engineering (miscellaneous)
  • Applied Mathematics
  • Computational Mechanics

Cite this

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abstract = "We use two meshless local Petrov-Galerkin (MLPG) formulations to analyse a heat conduction in a bimetallic circular disk. The continuity of the normal component of the heat flux at the interface between two materials is satisfied either by the method of Lagrange multipliers or by using a jump function. The convergence of the H0 and H1 error norms for the four numerical solutions with an increase in the number of equally spaced nodes and in the number of quadrature points is scrutinized. With an increase in the number of uniformly spaced nodes, the two error norms decrease monotonically for the MLPG5 formulation bur are essentially unchanged for the MLPG1 formulation. To our knowledge, this is the first study comparing the performance of the two methods of modelling a discontinuity in the gradient of a field variable at the interface between two different materials.",
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