An element free Galerkin method for nonlinear heat transfer with phase change in Qinghai–Tibet railway embankment

Since the element free Galerkin method (EFGM) is based on moving least-squares (MLS) interpolants, it requires only a mesh of nodes and a boundary description, which are beneficial to some problems with the moving boundary conditions, such as the transient temperature field problems with phase change. Because freezing and thawing often takes place in embankments in cold regions, the phase transition must be considered in heat transfer calculation. Therefore, in this paper, the EFGM is presented to solve the thermal problem involving phase change in permafrost embankment. In the calculation, the latent heat is considered using the enthalpy-based method and the essential boundary condition is enforced by the Lagrange multipliers method. The EFGM code has been written in the FORTRAN language for obtaining the numerical solution. The result shows that, compared with the finite element solution, EFGM has more advantages such as better agreement with the observational data, high convergence rate, simple pre-processing and post-processing, etc. in a word, these analyses support the proposition for employing such a method for nonlinear temperature field involving the phase change in the actual railway project on permafrost.