Calculating the single-domain heat conduction with heat source problem by virtual boundary meshfree Galerkin method

• The single-domain heat conduction with heat source problem is calculated by VBMGM.
• VBMGM has advantages of Galerkin method, boundary element method and meshfree method.
• The numerical meanings of the weighted values in VBMGM are clear.
• VBMGM is easily programmed and researched for some heat and mass transfer problems.

The virtual boundary meshfree Galerkin method (VBMGM) is presented to calculate the single-domain heat conduction with heat source problem. The virtual source function of the virtual boundary and the heat source in the computational domain both are interpolated by the radial basis function interpolation. The equation of the proposed method is obtained by the Galerkin method of the weighted residual methods. Consequently, VBMGM possesses the advantages of Galerkin method, boundary element method and meshfree method. And the numerical meanings of the weighted values in VBMGM, such as the partial derivative the temperature, the heat flux and the heat source expression, are definite. The detailed and specific equation of VBMGM is deducted. The numerical examples, namely the temperatures of the rectangular domain and the square domain, are computed. And the accuracy and the stability of the proposed method for the single-domain heat conduction with heat source problem are validated.