1974/06/01 by L. E. Goodrich, Goodrich, L. E.
Energy · #Geothermal Energy Systems and Applications #analyse numérique #boundary conditions #condition aux limites #couche de neige #geothermics #géothermique #numerical analysis #phase transformation #snow cover #transformation de phase
paper · pdf · doi:10.4224/40001206
openalex publication_date 1974/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Following a critical review of the different numerical methods for treating the one-dimensional heat equation ( Fourier equation), without and with latent heat, a new numerical scheme for the treatment of problems with phase change is presented. This scheme, which is based on a finite difference formulation of the boundary condition at the moving interface between the two phases, calculates directly and continuously the position of the phase plane as a function of time. The method takes complete account of the nonlinearity of the resulting equation, as well as of the differences in thermal properties on either side of the interface. Nevertheless, the formulation is such that simple Gaussian elimination may be used as solution technique for the simultaneous equations. No iteration is necessary. In consequence, the new method remains computationally efficient while giving results of very good accuracy. A FORTRAN language programme has been written using this scheme. This programme, which was designed specifically for application to a range of geothermal problems, has been written in a generalized fashion. A range of choice of boundary conditions, input and ouput data, and thermal parameters is available within the same programme. The programme also includes the possibility of treating the seasonal evolution of a surface snow cover. That programme has been published under separate cover.