SPH-FDM boundary for the analysis of thermal process in homogeneous media with a discontinuous interface

A SPH-FDM boundary method is proposed for the analysis of thermal process in homogeneous media with a discontinuous interface in this study, in which the smoothed particle hydrodynamics (SPH) method is used in the inner computational domain; and the finite difference method (FDM) is used as the function approximation near the boundary. This mixed method not only can improve the calculation accuracy under the first-type boundary conditions (i.e., Dirichlet), but also can convert the second- and third-type boundary conditions (i.e., Neumann and Robin) into the first-type boundary conditions in solving heat conduction problems of homogeneous media. As a result, a second-order accuracy can be achieved in the entire solution domain. The proposed SPH-FDM boundary method is applicable to the analysis of heat conduction in various media, including the problems with discontinuous interface in the computational domain and the solidification of materials with a moving phase transition boundary. Numerical results show that the proposed SPH-FDM boundary method overcomes the difficulties of the conventional SPH method in dealing with the second- and third-type boundary conditions and has a very high calculation accuracy.