Dual reciprocity boundary element method for convective-diffusive solid-liquid phase change problems, Part 1. Formulation

Abstract

A new dual reciprocity boundary element method for one-domain solving of the nonlinear convective-diffusive equation, as appears in one-phase continuum formulation of the energy transport in solid-liquid phase change systems, is described. Laplace equation fundamental solution weighting, straight line geometry and constant field shape functions on the boundary, finite-difference time discretization and scaled augmented thin plate spline global interpolation functions for transforming the domain integrals into a finite series of boundary integrals are employed in two dimensions and in axisymmetry. Iterations over the timestep are based on the Voller-Swaminathan scheme, upgraded to cope with the convective term. The technique could be applied to a wide range of solid-liquid phase change problems where finite volume or finite element solvers have been almost exclusively used in the past.