Boundary Integral Formulation Of General Source- Based Method For Convective-diffusive Solid-liquid Phase Change Problems

Abstract

A new one-domain dual reciprocity boundary integral method technique for solving one-phase continuum formulation of the convective-diffusive energy equation as appears when treating 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, Crank-Nicolson time discretization and thin plate splines for transforming the domain integrals into a finite series of boundary integrals are employed. 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.