Meshless local petrov-galerkin method for nonlinear heat conduction problems

H. Thakur, K.M. Singh, P.K. Sahoo

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

The meshless local Petrov-Galerkin (MLPG) method is an effective meshless method to solve partial differential equations. In this article, the MLPG method is used to solve nonlinear steady and transient heat conduction problems. The essential boundary condition is enforced by the method of direct interpolation. The moving least-squares (MLS) method is used for interpolation. Thermal conductivity of the material is assumed to be dependent on the temperature. An iterative procedure based on the predictor-corrector method is used. Time integration is performed using the method. Results are compared with the available exact solution and the solution by the finite-element method, and is found to be in good agreement.
Original languageEnglish
Pages (from-to)393-410
Number of pages18
JournalNumerical Heat Transfer, Part B: Fundamentals
Volume56
Issue number5
DOIs
Publication statusPublished - 2009

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Meshless Local Petrov-Galerkin Method
Galerkin method
Galerkin methods
Heat Conduction
Heat conduction
conductive heat transfer
interpolation
Interpolation
predictor-corrector methods
Interpolate
meshfree methods
Transient Heat Conduction
Predictor-corrector Methods
Moving Least Squares
Meshless Method
least squares method
Iterative Procedure
Time Integration
Thermal Conductivity
Least Square Method

Cite this

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abstract = "The meshless local Petrov-Galerkin (MLPG) method is an effective meshless method to solve partial differential equations. In this article, the MLPG method is used to solve nonlinear steady and transient heat conduction problems. The essential boundary condition is enforced by the method of direct interpolation. The moving least-squares (MLS) method is used for interpolation. Thermal conductivity of the material is assumed to be dependent on the temperature. An iterative procedure based on the predictor-corrector method is used. Time integration is performed using the method. Results are compared with the available exact solution and the solution by the finite-element method, and is found to be in good agreement.",
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Meshless local petrov-galerkin method for nonlinear heat conduction problems. / Thakur, H.; Singh, K.M.; Sahoo, P.K.

In: Numerical Heat Transfer, Part B: Fundamentals, Vol. 56, No. 5, 2009, p. 393-410.

Research output: Contribution to journalArticle

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PY - 2009

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AB - The meshless local Petrov-Galerkin (MLPG) method is an effective meshless method to solve partial differential equations. In this article, the MLPG method is used to solve nonlinear steady and transient heat conduction problems. The essential boundary condition is enforced by the method of direct interpolation. The moving least-squares (MLS) method is used for interpolation. Thermal conductivity of the material is assumed to be dependent on the temperature. An iterative procedure based on the predictor-corrector method is used. Time integration is performed using the method. Results are compared with the available exact solution and the solution by the finite-element method, and is found to be in good agreement.

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DO - 10.1080/10407790903508152

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JO - Numerical Heat Transfer, Part B: Fundamentals

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