Numerical Study of the 3D Variable Coefficient Heat Transfer Problem by Using the Finite Pointset Method

Abstract

In this paper, a parallel mesh-free finite pointset method (FPM) for the 3D variable coefficient transient heat conduction problem (I-FPM-3D) on regular/irregular region is proposed by coupling several techniques as follows. The partial differential equation with the high-order derivatives is first decomposed into several first-order equations to improve the numerical stability, reduce the computational complexity and easily enforce the Neumann boundary condition. Then, each first-order derivative is solved by the FPM repeatedly. Moreover, the MPI parallel technique is introduced to enhance the computational efficiency, and an appropriate Wendland kernel function is employed which has higher accuracy than the Gaussian function. 3D transient heat conduction problems with different boundary conditions, including the case in a complex cylindrical domain, are investigated and compared with the analytical solutions to illustrate the flexibility and the accuracy of the parallel I-FPM-3D. The convergence and the computational efficiency of the parallel I-FPM-3D are also analyzed. Finally, the temperature field in a 3D functional gradient material is predicted by the parallel I-FPM-3D and compared with the other numerical results. The numerical results indicate that the temperature variation process in the functional gradient materials can be visualized accurately.