Meshless Local B-Spline Basis Functions-FD Method and its Application for Heat Conduction Problem with Spatially Varying Heat Generation

In this paper, a new meshless local B-spline basis functions-finite difference (FD) method is presented for two-dimensional heat conduction problem with spatially varying heat generation. In the method, governing equations are discretized by B-spline approximation in the spirit of FD technique using local B-spline collocation. The key aspect of the method is that any derivative at a point or node is stated as neighbouring nodal values based on the B-spline interpolants. Compared with mesh-based method such as FEM the method is simple and efficient to program. In addition, as the method poses the Kronecker delta property, the imposition of boundary conditions is also easy and straightforward. Moreover, it poses no difficulties in dealing with arbitrary complex domains. Heat conduction problem in complex geometry is presented to demonstrate the accuracy and efficiency of the present method.