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A simple, effective and high-precision boundary meshfree method for solving 2D anisotropic heat conduction problems

Jing Ling1,2, Dongsheng Yang3,4

  • 1School of Materials and Architectural Engineering (Guizhou School of Emergency Management), Guizhou Normal University, Guiyang City, 550025, China.

Scientific Reports
|October 13, 2024
PubMed
Summary

A novel virtual boundary meshfree Galerkin method (VBMGM) accurately solves 2D anisotropic heat conduction problems. This high-precision approach is effective even for complex boundaries and requires fewer computational resources.

Keywords:
2D anisotropic heat conduction problemsComplex boundariesGalerkin methodHigh-precision boundary-type meshfree methodVirtual boundary element method

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Area of Science:

  • Computational Mechanics
  • Heat Transfer
  • Numerical Methods

Background:

  • Solving 2D anisotropic heat conduction problems with complex geometries presents significant computational challenges.
  • Existing numerical methods often struggle with accuracy and efficiency when dealing with intricate boundary conditions.

Purpose of the Study:

  • To introduce and validate a simple, effective, and high-precision boundary meshfree method for 2D anisotropic heat conduction.
  • To demonstrate the method's capability in handling complex boundaries and mixed boundary conditions.

Main Methods:

  • The Virtual Boundary Meshfree Galerkin Method (VBMGM) is employed, combining advantages of Galerkin, meshfree, and boundary element methods.
  • Temperature and heat flux are formulated using the virtual boundary element method.
  • Radial basis function interpolation is utilized to construct the virtual source function.

Main Results:

  • VBMGM demonstrated high precision in solving seven numerical examples of anisotropic heat conduction problems.
  • The method proved effective for problems with complex boundaries and mixed boundary conditions.
  • Computational efficiency was highlighted, with degrees of freedom often reduced by half compared to other methods.

Conclusions:

  • The Virtual Boundary Meshfree Galerkin Method (VBMGM) is a robust and accurate technique for 2D anisotropic heat conduction.
  • Its meshfree nature and boundary-focused approach simplify the handling of complex geometries.
  • VBMGM offers a promising alternative for efficient and precise thermal analysis in complex engineering applications.