An integral equation method for spherical Stefan problems

Many applications in solidification or melting are described by a two-phase Stefan problem with spherical symmetry. Using Green’s representation theorem, the heat equation is reformulated as a system of integral equations for the unknown fluxes on the interface. The unknown radius of the solid–liquid interface is determined from the Stefan condition. The integral equation is discretized with the Nyström method for which special singularity corrected quadrature rules are discussed. Numerical examples are presented that demonstrate the effectiveness of the method.