An element free Galerkin method for nonlinear heat transfer with phase change in Qinghai–Tibet railway embankment Gao Zhihua ⁎ , Lai Yuanming, Zhang Mingyi, Qi Jilin, Zhang Shujuan State Key Laboratory of Frozen Soil Engineering, Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Science, Lanzhou 730000, China Received 4 July 2006; accepted 17 October 2006 Abstract 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. © 2006 Elsevier B.V. All rights reserved. Keywords: Nonlinear temperature field; Qinghai–Tibet railway; The element free Galerkin method; Lagrange multiplier method 1. Introduction In cold regions, freezing and thawing occurs annu- ally. Thus, the heat transfer of the embankment on permafrost becomes a strongly nonlinear field problem with phase change. In the traditional analyses, such cases can be solved by either front-tracking methods (Hogge and Gerrekens, 1982) or fixed-grid methods. In the front-tracking methods, re-meshing will be needed in each step of the solution process because of the discontinuities which do not coincide with the original mesh lines. In the fixed-grid methods, the enthalpy method (Tamma and Namburu, 1990) and the apparent heat capacity method (Lai et al., 2004) have always been adopted. Although we can obtain high accuracy by these methods, any of them needs finite element mesh, which not only will lead to the complex pre-processing but also may cause mesh distortion. To avoid these problems, this paper will introduce the element free Galerkin method (Belytschko et al., 1994a) and deal with the two- dimensional nonlinear transient field problem of the Cold Regions Science and Technology 48 (2007) 15 – 23 www.elsevier.com/locate/coldregions ⁎ Corresponding author. Tel.: +86 931 4967282. E-mail addresses: zhgao@ns.lzb.ac.cn, gzh.hello@163.com (G. Zhihua). 0165-232X/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.coldregions.2006.10.004